A161952 Base-15 Armstrong or narcissistic numbers (written in base 10).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 113, 128, 2755, 3052, 5059, 49074, 49089, 386862, 413951, 517902, 15219156, 18605333, 38009273, 40082196, 40310423, 40868227, 47527794, 100128060, 100128061, 100128188, 104189152, 105464820

Offset: 1

Author

Joseph Myers, Jun 22 2009

Keywords

• base
• fini
• full
• nonn

Comments

Whenever 15|a(n) (n = 32, 36, 40, 86, 100, 135, 143, 194, 197, 201), then a(n+1) = a(n) + 1. Zero also satisfies the definition (n = Sum_{i=1..k} d[i]^k where d[1..k] are the base-15 digits of n), but this sequence only considers positive terms. - M. F. Hasler, Nov 22 2019

Links

• Joseph Myers, Table of n, a(n) for n = 1..202 (the full list of terms, from Winter)
• Henk Koppelaar and Peyman Nasehpour, On Hardy's Apology Numbers, arXiv:2008.08187 [math.NT], 2020.
• Eric Weisstein's World of Mathematics, Narcissistic Number
• D. T. Winter, Table of Armstrong Numbers

Crossrefs

In other bases: A010344 (base 4), A010346 (base 5), A010348 (base 6), A010350 (base 7), A010354 (base 8), A010353 (base 9), A005188 (base 10), A161948 (base 11), A161949 (base 12), A161950 (base 13), A161951 (base 14), A161953 (base 16).

Programs

Mathematica

Select[Range[10^7], # == Total[IntegerDigits[#, 15]^IntegerLength[#, 15]] &] (* Michael De Vlieger, Nov 04 2020 *)

PARI

select( is_A161952(n)={n==vecsum([d^#n|d<-n=digits(n,15)])}, [1..10^5]) \\ M. F. Hasler, Nov 22 2019

Extensions

Terms sorted in increasing order by Pontus von Brömssen, Mar 03 2019