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

%I A351374 #72 May 05 2025 16:38:24
%S A351374 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,2413,53808,760400,
%T A351374 760401,45661018,62470211,619939142,14613048357,1421043363262183,
%U A351374 48470736648305918,514822672411130775,360672575087017687943,264237343348909655564587,267218514330351511200145
%N A351374 Base-20 Armstrong or narcissistic numbers (written in base 10).
%C A351374 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.
%C A351374 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
%H A351374 Jinyuan Wang, <a href="/A351374/a351374.c.txt">C program</a>
%H A351374 Jinyuan Wang, <a href="https://drive.google.com/file/d/1hVEKKs1DIoOPyNas1Y0vtQyLs5hqHcEh/view?usp=sharing">Table of base-20 Armstrong numbers</a>
%H A351374 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NarcissisticNumber.html">Narcissistic Number</a>
%e A351374 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.)
%t A351374 Select[Range[10^6], # == Total[ IntegerDigits[#, 20]^IntegerLength[#, 20]] &]
%o A351374 (PARI) isok(m) = my(d=digits(m, 20)); sum(k=1, #d, d[k]^#d) == m; \\ _Michel Marcus_, Mar 19 2022
%o A351374 (Python)
%o A351374 from itertools import islice, combinations_with_replacement
%o A351374 from sympy.ntheory.factor_ import digits
%o A351374 def A351374_gen(): # generator of terms
%o A351374     for k in range(1,157):
%o A351374         a = tuple(i**k for i in range(20))
%o A351374         yield from (x[0] for x in sorted(filter(lambda x:x[0] > 0 and tuple(sorted(digits(x[0],20)[1:])) == x[1], \
%o A351374                           ((sum(map(lambda y:a[y],b)),b) for b in combinations_with_replacement(range(20),k)))))
%o A351374 A351374_list = list(islice(A351374_gen(),20)) # _Chai Wah Wu_, Apr 20 2022
%Y A351374 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), A161952 (base 15), A161953 (base 16).
%K A351374 nonn,base,fini
%O A351374 1,2
%A A351374 _Giovanni Corbelli_, Mar 18 2022
%E A351374 a(28)-a(30) from _Chai Wah Wu_, Apr 20 2022
%E A351374 a(31)-a(33) from _Jinyuan Wang_, May 05 2025