A250267 Least of 3 consecutive prime powers in arithmetic progression.

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

Table of n, a(n) for n=1..51.

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

Adjacent sequences: A250264 A250265 A250266 * A250268 A250269 A250270

Keyword

nonn

Author

Michel Marcus, Nov 16 2014

Status

approved