A335205 Numbers of m digits which are equal to the absolute value of the sum of the m-th powers of their digits, with alternating signs.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 48, 407, 5920, 5921, 2918379, 18125436, 210897052, 11647261846, 18107015789, 27434621679, 31332052290, 4986706842391, 485927682264092, 1287253463537089, 1217506990394433558, 11008589751726485523, 107765279704274410345, 109462377410000145640, 109462377410000145641, 118620909850977982494, 319591187568367788829

Offset

1,3

Comments

Numbers n equal to |Sum_{j=1..k} (-1)^j*d_j^k| where d_1 d_2 ... d_k is the decimal expansion of n. A variant of narcissistic numbers (A005188), they are finite as well.

The last term is smaller than 1.2*10^50. - Jinyuan Wang, May 28 2020

Note that a(14) = a(13) + 1, a(29) = a(28) + 1 - Chai Wah Wu, Jun 03 2020

Links

Table of n, a(n) for n=1..31.

Example

5921 is a term because |5^4 - 9^4 + 2^4 - 1^4| = 5921.

Mathematica

s[n_] := Block[{d = IntegerDigits@ n}, Abs@ Total[d^Length[d] (-1)^Range@ Length@ d]]; Select[ Range[0, 3*10^6], s[#] == # &]

Prog

(PARI) is(k)= my(v=digits(k)); abs(sum(i=1, #v, (-1)^i*v[i]^#v))==k; \\ Jinyuan Wang, May 28 2020

Crossrefs

Cf. A005188, A335151.

Sequence in context: A257829 A219327 A219326 * A349190 A252781 A024660

Adjacent sequences: A335202 A335203 A335204 * A335206 A335207 A335208

Keyword

nonn,base,fini,more

Author

Giovanni Resta, May 26 2020

Extensions

a(24)-a(25) from Chai Wah Wu, May 31 2020

a(26) from Chai Wah Wu, Jun 01 2020

a(27)-a(31) from Chai Wah Wu, Jun 03 2020

Status

approved