A161951 Base-14 Armstrong or narcissistic numbers (written in base 10).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 244, 793, 282007, 10362564, 1445712420, 29546248981, 164159496751, 342515735622, 359057049845, 216210334578515, 324075236456868, 338527182572746, 338609726265795, 382789516519507

Offset

1,2

Comments

Whenever 14|a(n) (n = 36, 46, 75, 77), 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-14 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..103 (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

Mathematica

Select[Range[2 * 10^7], # == Total[IntegerDigits[#, 14]^IntegerLength[#, 14]] &] (* Michael De Vlieger, Nov 04 2020 *)

Prog

(PARI) select( is_A161951(n)={n==vecsum([d^#n|d<-n=digits(n, 14)])}, [1..10^6\3]) \\ M. F. Hasler, Nov 22 2019

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), A161952 (base 15), A161953 (base 16).

Sequence in context: A055647 A043318 A044915 * A290492 A191431 A191430

Adjacent sequences: A161948 A161949 A161950 * A161952 A161953 A161954

Keyword

base,fini,full,nonn

Author

Joseph Myers, Jun 22 2009

Status

approved