A344990 Primes of the form m^k +- k, with m,k > 1.

2, 5, 7, 11, 23, 37, 47, 61, 67, 79, 83, 167, 223, 227, 359, 439, 443, 503, 509, 521, 727, 839, 997, 1019, 1087, 1091, 1223, 1367, 1523, 1847, 2027, 2207, 2399, 2741, 3023, 3251, 3719, 3967, 4093, 4099, 4759, 5039, 5623, 5927, 6553, 6563, 6569, 7919, 8179

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

    2 =  2^2 - 2,
    5 =  2^3 - 3,
    7 =  3^2 - 2,
   11 =  3^2 + 2,
   23 =  5^2 - 2,
   37 =  2^5 + 5,
   47 =  7^2 - 2,
   61 =  4^3 - 3,
   67 =  4^3 + 3,
   79 =  9^2 - 2,
   83 =  9^2 + 2,
  167 = 13^2 - 2,
  223 = 15^2 - 2,
  227 = 15^2 + 2,
  359 = 19^2 - 2,
  439 = 21^2 - 2,
  443 = 21^2 + 2,
  503 =  2^9 - 9,
  509 =  8^3 - 3,
  521 =  2^9 + 9,
  ...

Maple

N:= 10000: # for terms <= N
S:= {2}:
for m from 2 while m^2-2 <= N do
  for k from 3-(m mod 2) by 2 do
    v:= m^k-k;
    if v > N then break fi;
    if isprime(v) then S:= S union {v} fi;
    v:= m^k + k;
    if v <= N and isprime(v) then S:= S union {v} fi;
od od:
sort(convert(S, list)); # Robert Israel, Mar 02 2026

Crossrefs

Union of A099227 and A099228.

Sequence in context: A038955 A172981 A141064 * A131102 A235468 A229209

Adjacent sequences: A344987 A344988 A344989 * A344991 A344992 A344993

Keyword

nonn

Author

Luke Voyles, Jun 05 2021

Status

approved