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.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 370, 5295, 8208, 54900, 54901, 417889, 136151168, 9905227379, 282185923199, 2527718648914, 14441494066365380, 14441494066365381, 12317155720243258398, 13393750378644587854
Offset: 1
Examples
370 = |3^3 + 7^3 - 0^3|. 5295 = |5^4 + 2^4 - 9^4 + 5^4|. 8208 = |8^4 + 2^4 - 0^4 + 8^4|. 54900 = |5^5 + 4^5 - 9^5 + 0^5 - 0^5|. 54901 = |5^5 + 4^5 - 9^5 + 0^5 - 1^5|.
Programs
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Mathematica
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 *) -
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
Extensions
a(18)-a(20) from Giovanni Resta, May 25 2020
a(21)-a(22) from Chai Wah Wu, May 31 2020
a(23)-a(24) from Chai Wah Wu, Jun 01 2020
Comments