A329595 -id:A329595 - cp's OEIS frontend

1, 2, 3, 8, 10, 24, 28, 48, 80, 82, 126, 168, 224, 226, 242, 360, 440, 442, 728, 840, 1088, 1090, 1224, 1368, 1522, 1848, 2026, 2208, 2400, 3024, 3250, 3374, 3720, 3968, 4760, 5040, 5624, 5928, 6562, 6858, 7920, 8648, 9802, 10608, 11026, 11448, 12322, 13688, 13690, 14160, 14640, 15130, 16128, 17160

Offset: 1

S. Brunner, Nov 17 2019

nonn

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.
If only perfect powers other than 0 and 1 were allowed, then this sequence would start with 3.
All terms greater than 3 are even and follow or precede an odd power.

			The first 20 terms with their neighbors:
   n  k-1  k k+1      |       n  k-1  k   k+1
   1  0^2  1   2      |      11  5^3 126  127
   2  1^2  2   3      |      12  167 168 13^2
   3    2  3 2^2      |      13  223 224 15^2
   4    7  8 3^2      |      14 15^2 226  227
   5  3^2 10  11      |      15  241 242  3^5
   6   23 24 5^2      |      16  359 360 19^2
   7  3^3 28  29      |      17  439 440 21^2
   8   47 48 7^2      |      18 21^2 442  443
   9   79 80 3^4      |      19  727 728  3^6
  10  3^4 82  83      |      20  839 840 29^2

S. Brunner, Table of n, a(n) for n = 1..1600

Cf. A163492, A329595.

isok(k) = (k==1) || (k==2) || (ispower(k-1) && isprime(k+1)) || (isprime(k-1) && ispower(k+1)); \\ Michel Marcus, Nov 18 2019

cp's OEIS Frontend

A329582 Numbers between a power and a prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI