{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:27:33Z","timestamp":1750307253375,"version":"3.41.0"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2011,6,1]],"date-time":"2011-06-01T00:00:00Z","timestamp":1306886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Inroads"],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p>\n            This article explores various optimizations that can be used to speed the discovery of Armstrong numbers (also known as Narcissistic numbers), which are\n            <jats:italic>n<\/jats:italic>\n            -digit numbers that are the sum of the\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>th<\/jats:sup>\n            powers of their digits. Optimizations include comparing the parity of the least-significant digit of the number and that of the sum of its digits, using a dynamic programming approach for the powers of digits, examining the parity of the sum of digits excluding the least-significant digit, and computing forward bounds on the possible numbers and on the possible sums of\n            <jats:italic>d<\/jats:italic>\n            <jats:sub>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sub>\n            . The final optimization completes in about 2% of the time of the initial implementation.\n          <\/jats:p>","DOI":"10.1145\/1963533.1963548","type":"journal-article","created":{"date-parts":[[2012,10,15]],"date-time":"2012-10-15T19:22:23Z","timestamp":1350328943000},"page":"43-46","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimizations generating Armstrong numbers"],"prefix":"10.1145","volume":"2","author":[{"given":"Timothy J.","family":"Rolfe","sequence":"first","affiliation":[{"name":"Eastern Washington University, Cheney, Washington"}]}],"member":"320","published-online":{"date-parts":[[2011,6]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Weisstein Eric W. \"Narcissistic Number.\" From MathWorld--A Wolfram Web Resource. http:\/\/mathworld.wolfram.com\/NarcissisticNumber.html. Accessed 2010 December 15.  Weisstein Eric W. \"Narcissistic Number.\" From MathWorld--A Wolfram Web Resource. http:\/\/mathworld.wolfram.com\/NarcissisticNumber.html. Accessed 2010 December 15."},{"key":"e_1_2_1_2_1","unstructured":"G.H. Hardy A Mathematician's Apology (First Electronic Edition Version 1.0; University of Alberta Mathematical Sciences Society March 2005) pp. 24--25. Accessible through http:\/\/www.math.ualberta.ca\/~mss\/misc\/A%20Mathematician's%20Apology.pdf. Accessed 2010 December 20.  G.H. Hardy A Mathematician's Apology (First Electronic Edition Version 1.0; University of Alberta Mathematical Sciences Society March 2005) pp. 24--25. Accessible through http:\/\/www.math.ualberta.ca\/~mss\/misc\/A%20Mathematician's%20Apology.pdf. Accessed 2010 December 20."},{"volume-title":"Old Testament translation by J.M.Powis Smith et al., the Apocrypha and New Testament translated by","year":"1939","author":"John","key":"e_1_2_1_3_1"},{"key":"e_1_2_1_4_1","unstructured":"Lionel Deimel http:\/\/www.deimel.org\/rec_math\/DI_0.htm. Access 2010 December 20.  Lionel Deimel http:\/\/www.deimel.org\/rec_math\/DI_0.htm. Access 2010 December 20."},{"key":"e_1_2_1_5_1","first-page":"36","author":"Gardner Martin","year":"1976","journal-title":"Charles Scribner's Sons"},{"key":"e_1_2_1_6_1","unstructured":"Lionel Deimel http:\/\/www.deimel.org\/rec_math\/DI_6.htm. Accessed 2010 December 20.  Lionel Deimel http:\/\/www.deimel.org\/rec_math\/DI_6.htm. Accessed 2010 December 20."},{"key":"e_1_2_1_7_1","unstructured":"http:\/\/www.deimel.org\/rec_math\/armstrong.pdf. Accessed 2010 December 20.  http:\/\/www.deimel.org\/rec_math\/armstrong.pdf. Accessed 2010 December 20."},{"key":"e_1_2_1_8_1","first-page":"956","volume-title":"Introduction to the Design and Analysis of Algorithms","author":"Levitin Anany","year":"2007","edition":"2"},{"key":"e_1_2_1_9_1","first-page":"272","volume-title":"Algorithms","author":"Sanjoy Dasgupta","year":"2008"},{"key":"e_1_2_1_10_1","unstructured":"http:\/\/en.wikipedia.org\/wiki\/Narcissistic_number. Accessed 2010 December 20.  http:\/\/en.wikipedia.org\/wiki\/Narcissistic_number. Accessed 2010 December 20."}],"container-title":["ACM Inroads"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1963533.1963548","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1963533.1963548","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T10:52:19Z","timestamp":1750243939000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1963533.1963548"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,6]]}},"alternative-id":["10.1145\/1963533.1963548"],"URL":"https:\/\/doi.org\/10.1145\/1963533.1963548","relation":{},"ISSN":["2153-2184","2153-2192"],"issn-type":[{"type":"print","value":"2153-2184"},{"type":"electronic","value":"2153-2192"}],"subject":[],"published":{"date-parts":[[2011,6]]},"assertion":[{"value":"2011-06-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}