A250268 - OEIS

%I #15 Jan 07 2018 21:35:55

%S 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,

%T 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,

%U 6,6,12,6,6,6,6,6,6,6,12,6,6,6,12,12,6,12

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

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

%H Laurentiu Panaitopol, <a href="https://projecteuclid.org/euclid.rmjm/1181070157">Some of the properties of the sequence of powers of prime numbers</a>, Rocky Mountain Journal of Mathematics, Volume 31, Number 4, Winter 2001.

%e Common differences of consecutive prime powers in arithmetic progression up to 100:

%e 1:  1  2  3

%e 1:  2  3  4

%e 1:  3  4  5

%e 1:  7  8  9

%e 2:  9 11 13

%e 2: 23 25 27

%e 2: 25 27 29

%e 2: 27 29 31

%e 3: 61 64 67

%e 2: 79 81 83

%o (PARI) ispp(n) = isprimepower(n) || (n==1);

%o 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], ", ")););}

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

%Y Cf. A250267.

%K nonn

%O 1,5

%A _Michel Marcus_, Nov 16 2014