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

Author

Giovanni Resta, May 26 2020

Keywords

• nonn
• base
• fini
• more

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

Examples

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

Crossrefs

Cf. A005188, A335151.

Programs

Mathematica

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

PARI

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