A329582 Numbers between a power and a prime.

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

1,2

Comments

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.

Links

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

Example

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

Prog

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

Crossrefs

Cf. A163492, A329595.

Sequence in context: A098844 A034437 A175715 * A138880 A063474 A163492

Adjacent sequences: A329579 A329580 A329581 * A329583 A329584 A329585

Keyword

nonn

Author

S. Brunner, Nov 17 2019

Status

approved