A259394 Primes of the form (sum of the digits of k to consecutive powers starting at 1) + k, ordered by k (duplicates allowed).

2, 11, 13, 17, 23, 31, 41, 53, 67, 83, 101, 53, 89, 61, 67, 97, 127, 79, 83, 89, 97, 107, 149, 167, 101, 101, 103, 131, 839, 127, 193, 347, 863, 157, 167, 379, 677, 197, 199, 227, 419, 547, 313, 467, 983, 223, 281, 563, 733, 241, 251, 271, 463, 761, 277, 307, 499, 797, 331, 389

Offset

1,1

Links

Table of n, a(n) for n=1..60.

Matematico Fresnillense, Bella Curiosidad Matematica

Example

For 10<=n<=19,
10 -> 1^1 + 0^2 + 10 = 11
11 -> 1^1 + 1^2 + 11 = 13
12 -> 1^1 + 2^2 + 12 = 17
13 -> 1^1 + 3^2 + 13 = 23
14 -> 1^1 + 4^2 + 14 = 31
15 -> 1^1 + 5^2 + 15 = 41
16 -> 1^1 + 6^2 + 16 = 53
17 -> 1^1 + 7^2 + 17 = 67
18 -> 1^1 + 8^2 + 18 = 83
19 -> 1^1 + 9^2 + 19 = 101

Maple

f:= proc(k) local L, j;
  L:= convert(k, base, 10);
  add(L[-i]^i, i=1..nops(L))+k
end proc:
select(isprime, map(f, [$1..1000])); # Robert Israel, Jul 13 2015

Mathematica

f[n_] := Block[{d = IntegerDigits[n], p},
  p = n + Total[d^Range[Length[d]]]; If[PrimeQ@p, p, {}]];
Array[f, 300] // Flatten (* Robert G. Wilson v, Jul 12 2015 *)

Prog

(PARI) f(n)={my(v=digits(n), k=#v, i, j=n); for(i=1, k, j+=v[i]^i); return(j); }
main(size)={my(v=vector(size), i, t=1); for(i=1, size, while(!isprime(f(t)), t++); v[i]=f(t); t++); v; } /* Anders Hellström, Jul 13 2015 */

Crossrefs

Sequence in context: A338976 A160950 A141168 * A079132 A184802 A023257

Adjacent sequences: A259391 A259392 A259393 * A259395 A259396 A259397

Keyword

nonn,base

Author

José de Jesús Camacho Medina, Jun 25 2015

Status

approved