cp's OEIS Frontend

A335151 Numbers m equal to |d_1^k + Sum_{j=2..k} (-1)^j*d_j^k| where d_1 d_2 ... d_k is the decimal expansion of m.

%I A335151 #19 Jun 01 2020 17:22:45
%S A335151 0,1,2,3,4,5,6,7,8,9,370,5295,8208,54900,54901,417889,136151168,
%T A335151 9905227379,282185923199,2527718648914,14441494066365380,
%U A335151 14441494066365381,12317155720243258398,13393750378644587854
%N A335151 Numbers m equal to |d_1^k + Sum_{j=2..k} (-1)^j*d_j^k| where d_1 d_2 ... d_k is the decimal expansion of m.
%C A335151 In other words: m = |digit1^k + digit2^k - digit3^k + digit4^k -...+/- lastdigit^k|, where k is the number of digits. Note that the sign of the first two addends is always positive.
%C A335151 Concept derived from the Armstrong numbers (A005188).
%C A335151 Note that a(15) = a(14) + 1 and a(22) = a(21) + 1. - _Chai Wah Wu_, May 31 2020
%e A335151 370 = |3^3 + 7^3 - 0^3|.
%e A335151 5295 = |5^4 + 2^4 - 9^4 + 5^4|.
%e A335151 8208 = |8^4 + 2^4 - 0^4 + 8^4|.
%e A335151 54900 = |5^5 + 4^5 - 9^5 + 0^5 - 0^5|.
%e A335151 54901 = |5^5 + 4^5 - 9^5 + 0^5 - 1^5|.
%t A335151 ss[n_] := ss[n] = Join[{1}, -(-1)^Range[n-1]]; Select[ Range[0, 500000], (d = IntegerDigits[#]; # == Abs@ Total[d^Length[d] ss@ Length@ d]) &] (* _Giovanni Resta_, May 25 2020 *)
%o A335151 (PARI) is(k) = my(v=digits(k)); !k || abs(v[1]^#v + sum(i=2, #v, (-1)^i*v[i]^#v))==k; \\ _Jinyuan Wang_, May 28 2020
%Y A335151 Cf. A005188, A335205.
%K A335151 nonn,base,fini,more
%O A335151 1,3
%A A335151 _Lukas R. Mansour_, May 25 2020
%E A335151 a(18)-a(20) from _Giovanni Resta_, May 25 2020
%E A335151 a(21)-a(22) from _Chai Wah Wu_, May 31 2020
%E A335151 a(23)-a(24) from _Chai Wah Wu_, Jun 01 2020