A243023 Consider a k-digit number m = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + ... + d_(2)*10 + d_(1). Sequence lists the numbers m that divide Sum_{i=1..k-1}{d_(i+1)^d(i)}+d(1)^d(k) (see example below).

1, 2, 3, 4, 5, 6, 7, 8, 9, 63, 448, 1547, 1693, 6189068, 20443796, 67526389

Offset

1,2

Comments

Numbers with two consecutive zeros are not considered, to avoid the case 0^0. Nevertheless, even if we consider 0^0=1 the results do not change (at least up to the last number I tested, that is m=10^8).

Links

Table of n, a(n) for n=1..16.

Example

For 63 we have 6^3 + 3^6 = 945 and 945/63 = 15.
Obviously also with 36 we have 3^6 + 6^3 = 945 but 945/36 = 105/4.
For 6189068 we have: 6^8 + 0^6 + 9^0 + 8^9 + 1^8 + 6^1 + 8^6 = 136159496.
Finally 136159496/6189068 = 22.

Maple

with(numtheory): P:=proc(q) local a, b, k, ok, n; for n from 10 to q do a:=[]; b:=n;
while b>0 do a:=[op(a), b mod 10]; b:=trunc(b/10); od; b:=0; ok:=1; for k from 2 to nops(a)
do if a[k-1]=0 and a[k]=0 then ok:=0; break; else b:=b+a[k]^a[k-1]; fi; od;
if ok=1 then if type((b+a[1]^a[nops(a)])/n, integer) then print(n);
fi; fi; od; end: P(10^10);

Mathematica

fQ[n_] := Block[{id = IntegerDigits@ n}, IntegerQ[ Total[ (id^RotateLeft@ id)]/n]]; k = 1; lst = {}; While[k < 1000000001, If[fQ@k, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G. Wilson v, Jun 01 2014 *)

Crossrefs

Cf. A243024, A243025.

Sequence in context: A107070 A320081 A243507 * A243024 A004860 A302499

Adjacent sequences: A243020 A243021 A243022 * A243024 A243025 A243026

Keyword

nonn,base,fini,full

Author

Paolo P. Lava, May 29 2014

Status

approved