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

1,3

Comments

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.

Concept derived from the Armstrong numbers (A005188).

Note that a(15) = a(14) + 1 and a(22) = a(21) + 1. - Chai Wah Wu, May 31 2020

Links

Table of n, a(n) for n=1..24.

Example

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|.

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 *)

Prog

(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

Crossrefs

Cf. A005188, A335205.

Sequence in context: A308110 A306593 A046469 * A065110 A307887 A362843

Adjacent sequences: A335148 A335149 A335150 * A335152 A335153 A335154

Keyword

nonn,base,fini,more

Author

Lukas R. Mansour, May 25 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

Status

approved