A329595 Numbers k such that either (a) k-1=i^m for some i and m >= 3 and k+1 is a prime, or (b) k-1 is a prime and k+1 = i^m for some i and m >= 3.

1, 2, 28, 80, 82, 126, 242, 728, 2400, 3374, 6562, 6858, 14640, 19682, 24390, 28560, 29790, 50626, 50652, 59050, 91126, 161052, 194480, 194482, 250048, 274626, 300762, 328510, 357912, 371292, 571788, 707280, 753570, 759376, 823542, 970298, 1157626, 1295028, 1442898, 1771560, 1860868, 2146688, 2146690

Offset

1,2

Comments

If 0 or 1 are not counted as powers, then this sequence starts with 28.

All terms other than 1 are even and follow or precede an odd power.

Links

S. Brunner, Table of n, a(n) for n = 1..1100

Example

The first 20 terms with their neighbors:
   n  k-1   k   k+1      |       n   k-1    k    k+1
   1  0^3    1    2      |      11   3^8  6562  6563
   2  1^3    2    3      |      12  6857  6858  19^3
   3  3^3   28   29      |      13 14639 14640  11^4
   4   79   80  3^4      |      14 19681 19682   3^9
   5  3^4   82   83      |      15  29^3 24390 24391
   6  5^3  126  127      |      16 28559 28560  13^4
   7  241  242  3^5      |      17 29789 29790  31^3
   8  727  728  3^6      |      18  15^4 50626 50627
   9 2399 2400  7^4      |      19 50651 50652  37^3
  10 3373 3374 15^3      |      20  3^10 59050 59051

Mathematica

{1, 2}~Join~Flatten@ Map[Which[AllTrue[{#2, #3}, # > 2 &], #1 + {-1, 1}, #2 > 2, #1 - 1, #3 > 2, #1 + 1, True, Nothing] & @@ Prepend[Map[GCD @@ FactorInteger[#][[All, -1]] &, {# - 2, # + 2}], #] &, Prime@ Range[160000]] (* Michael De Vlieger, Dec 27 2019 *)

Prog

(PARI) isok(k) = (k==1) || (k==2) || ((ispower(k-1) >= 3) && isprime(k+1)) || (isprime(k-1) && (ispower(k+1) >= 3)); \\ Michel Marcus, Nov 18 2019

Crossrefs

Cf. A163492, A329582.

Sequence in context: A245801 A296245 A156471 * A138964 A200040 A334696

Adjacent sequences: A329592 A329593 A329594 * A329596 A329597 A329598

Keyword

nonn

Author

S. Brunner, Nov 17 2019

Status

approved