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A250268
Common differences of consecutive prime powers that form a 3-term arithmetic progression.
0
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
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: A364721 A374480 A185617 * A342881 A292137 A292138
KEYWORD
nonn
AUTHOR
Michel Marcus, Nov 16 2014
STATUS
approved