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A250267
Least of 3 consecutive prime powers in arithmetic progression.
1
1, 2, 3, 7, 9, 23, 25, 27, 61, 79, 151, 199, 239, 257, 331, 361, 367, 557, 587, 601, 619, 647, 941, 971, 1097, 1117, 1181, 1217, 1499, 1669, 1741, 1747, 1901, 2281, 2411, 2671, 2897, 2957, 3301, 3307, 3631, 3721, 3727, 4007, 4093, 4397, 4451, 4591, 4651, 4679, 4987
OFFSET
1,2
COMMENTS
This sequence is motivated by the article by L. Panaitopol. Actually he defines q(n) = A000961(n-1), and Q(n) = q(n+1)-2*q(n)+q(n-1). Then he asks if the sequence of indices n such that Q(n)=0 is infinite.
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
In A000961, 7 is followed by 8 and 9, a 3-term arithmetic progression with a common difference 1.
9 is followed by 11 and 13, a 3-term arithmetic progression with a common difference 2.
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-1], ", ")); ); }
CROSSREFS
Cf. A000961 (prime powers), A057820 (common differences of consecutive prime powers).
Sequence in context: A057239 A319911 A024541 * A333517 A207643 A205488
KEYWORD
nonn
AUTHOR
Michel Marcus, Nov 16 2014
STATUS
approved