cp's OEIS Frontend

A329582 Numbers between a power and a prime.

%I A329582 #39 Jan 05 2020 13:05:47
%S A329582 1,2,3,8,10,24,28,48,80,82,126,168,224,226,242,360,440,442,728,840,
%T A329582 1088,1090,1224,1368,1522,1848,2026,2208,2400,3024,3250,3374,3720,
%U A329582 3968,4760,5040,5624,5928,6562,6858,7920,8648,9802,10608,11026,11448,12322,13688,13690,14160,14640,15130,16128,17160
%N A329582 Numbers between a power and a prime.
%C A329582 All numbers k where k - 1 is any power with exponent greater than or equal to 2 and k + 1 is a prime number, or vice versa.
%C A329582 If only perfect powers other than 0 and 1 were allowed, then this sequence would start with 3.
%C A329582 All terms greater than 3 are even and follow or precede an odd power.
%H A329582 S. Brunner, <a href="/A329582/b329582.txt">Table of n, a(n) for n = 1..1600</a>
%e A329582 The first 20 terms with their neighbors:
%e A329582    n  k-1  k k+1      |       n  k-1  k   k+1
%e A329582    1  0^2  1   2      |      11  5^3 126  127
%e A329582    2  1^2  2   3      |      12  167 168 13^2
%e A329582    3    2  3 2^2      |      13  223 224 15^2
%e A329582    4    7  8 3^2      |      14 15^2 226  227
%e A329582    5  3^2 10  11      |      15  241 242  3^5
%e A329582    6   23 24 5^2      |      16  359 360 19^2
%e A329582    7  3^3 28  29      |      17  439 440 21^2
%e A329582    8   47 48 7^2      |      18 21^2 442  443
%e A329582    9   79 80 3^4      |      19  727 728  3^6
%e A329582   10  3^4 82  83      |      20  839 840 29^2
%o A329582 (PARI) isok(k) = (k==1) || (k==2) || (ispower(k-1) && isprime(k+1)) || (isprime(k-1) && ispower(k+1)); \\ _Michel Marcus_, Nov 18 2019
%Y A329582 Cf. A163492, A329595.
%K A329582 nonn
%O A329582 1,2
%A A329582 _S. Brunner_, Nov 17 2019