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

Author

Lukas R. Mansour, May 25 2020

Keywords

• nonn
• base
• fini
• more

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

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|.
		

Crossrefs

Cf. A005188, A335205.

Programs

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