A161952 -id:A161952 - cp's OEIS frontend

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, 435198066019184, 526088332647250

Offset: 1

Joseph Myers, Jun 22 2009

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

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

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).

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

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

A351374 Base-20 Armstrong or narcissistic numbers (written in base 10).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2413, 53808, 760400, 760401, 45661018, 62470211, 619939142, 14613048357, 1421043363262183, 48470736648305918, 514822672411130775, 360672575087017687943, 264237343348909655564587, 267218514330351511200145

Offset: 1

Giovanni Corbelli, Mar 18 2022

Written in base twenty the numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J, 60D, 6EA8, 4F100, 4F101, E57CAI, JA8FAB, 9DEC7H2, B86BB0HH.

Sequence is finite. Since k*19^k < 20^(k-1) for k >= 157, all terms must have less than 157 base-20 digits. 20*m is a term if and only if 20*m+1 is a term. - Chai Wah Wu, Apr 20 2022

			2413 is in the sequence because 2413 is 60D in base 20 (D stands for 13) and 6^3 + 0^3 + 13^3 = 2413. (The exponent 3 is the number of base-20 digits.)

Jinyuan Wang, C program
Jinyuan Wang, Table of base-20 Armstrong numbers
Eric Weisstein's World of Mathematics, Narcissistic Number

Select[Range[10^6], # == Total[ IntegerDigits[#, 20]^IntegerLength[#, 20]] &]

isok(m) = my(d=digits(m, 20)); sum(k=1, #d, d[k]^#d) == m; \\ Michel Marcus, Mar 19 2022

from itertools import islice, combinations_with_replacement
from sympy.ntheory.factor_ import digits
def A351374_gen(): # generator of terms
    for k in range(1,157):
        a = tuple(i**k for i in range(20))
        yield from (x[0] for x in sorted(filter(lambda x:x[0] > 0 and tuple(sorted(digits(x[0],20)[1:])) == x[1], \
                          ((sum(map(lambda y:a[y],b)),b) for b in combinations_with_replacement(range(20),k)))))
A351374_list = list(islice(A351374_gen(),20)) # Chai Wah Wu, Apr 20 2022

a(28)-a(30) from Chai Wah Wu, Apr 20 2022

a(31)-a(33) from Jinyuan Wang, May 05 2025

cp's OEIS Frontend

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

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