A250268 Common differences of consecutive prime powers that form a 3-term arithmetic progression.

1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 6, 12, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 12, 6, 6, 6, 12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 6, 6, 6, 6, 6, 6, 6, 12, 6, 6, 6, 12, 12, 6, 12

Offset

1,5

Comments

Subsequence of A057820: a term here corresponds to 3 equal consecutive terms of A057820.

Links

Table of n, a(n) for n=1..84.

Laurentiu Panaitopol, Some of the properties of the sequence of powers of prime numbers, Rocky Mountain Journal of Mathematics, Volume 31, Number 4, Winter 2001.

Example

Common differences of consecutive prime powers in arithmetic progression up to 100:
1:  1  2  3
1:  2  3  4
1:  3  4  5
1:  7  8  9
2:  9 11 13
2: 23 25 27
2: 25 27 29
2: 27 29 31
3: 61 64 67
2: 79 81 83

Prog

(PARI) ispp(n) = isprimepower(n) || (n==1);
lista(nn) = {v = select(x->ispp(x), vector(nn, i, i)); for (k=2, #v-1, if (v[k+1] - 2*v[k] + v[k-1] == 0, print1(v[k]-v[k-1], ", ")); ); }

Crossrefs

Cf. A000961 (prime powers), A057820 (common differences of consecutive prime powers).

Cf. A250267.

Sequence in context: A323246 A364721 A185617 * A342881 A292137 A292138

Adjacent sequences: A250265 A250266 A250267 * A250269 A250270 A250271

Keyword

nonn

Author

Michel Marcus, Nov 16 2014

Status

approved