A245387 Numbers k for which the alternating sum of the digits of k^k is +-1.

1, 5, 10, 20, 21, 43, 56, 78, 80, 100, 131, 160, 170, 215, 230, 300, 355, 485, 505, 540, 692, 824, 1000, 1055, 1165, 1335, 1340, 1429, 1453, 1505, 1739, 2102, 2309, 2740, 2936, 3772, 3972, 4055, 4489, 4676, 5080, 5512, 5600, 5660, 5700, 5770, 5796, 6350, 7173, 7512, 7790, 8372, 9380, 9767, 10000

Offset

1,2

Comments

k may be present only if k^k == +-1 (mod 11).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..400 (first 164 terms from Anthony Sand and Robert G. Wilson v)

Example

5 is a member since 5^5 = 3125 -> 3 - 1 + 2 - 5 = -1.

Mathematica

fQ[n_] := Block[{id = IntegerDigits[n^n]}, Abs[ Sum[id[[i]]*(-1)^i, {i, Length@ id}]] == 1]; k = 1; lst = {}; While[k < 10001, If[ fQ@ k, AppendTo[lst, k]]; k++]; lst

Prog

(PARI) is(n)=n=digits((n/10^valuation(n, 10))^n); abs(sum(i=1, #n, (-1)^i*n[i]))==1
forstep(n=1, 1e6, [4, 5, 2, 3, 5, 1, 2, 2, 5, 2, 2, 1, 5, 3, 2, 5, 4, 2, 4, 5, 2, 3, 5, 1, 2, 2, 5, 2, 2, 1, 5, 3, 2, 5, 4, 2], if(is(n), print1(n", "))) \\ Charles R Greathouse IV, Jul 22 2014

Crossrefs

Cf. A244212, A244144.

Sequence in context: A115825 A115774 A062052 * A115799 A072703 A086761

Adjacent sequences: A245384 A245385 A245386 * A245388 A245389 A245390

Keyword

nonn,base

Author

Anthony Sand and Robert G. Wilson v, Jul 20 2014

Status

approved