OFFSET
1,1
COMMENTS
Conjecture: Primitive prime powers are primes.
EXAMPLE
The first few terms of the sequence are the minuends in the following differences. The differences are strictly increasing by definition.
5 - 3 = 2;
17 - 13 = 4;
37 - 31 = 6;
97 - 89 = 8;
149 - 139 = 10;
211 - 199 = 12;
307 - 293 = 14;
907 - 887 = 20.
The example above might suggest the subtrahends are also prime. In general they are not, as the example a(10) shows, where 1361 - 1331 = 30, but 1331 is not prime. - Ivan N. Ianakiev, Feb 02 2023
MATHEMATICA
a[1] = 5; candidates[n_] := Select[Range[NextPrime[n, -1], n], OddQ[#] && PrimePowerQ[#]&];
difference[n_] := candidates[n][[-1]] - candidates[n][[-2]];
a[n_] := a[n] = Module[{k = a[n-1]+2}, While[OddQ[k] && !PrimePowerQ[k] || difference[k] <= difference[a[n-1]], k = k+2]; k];
a/@Range[16] (* Ivan N. Ianakiev, Feb 02 2023 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Feb 01 2023
STATUS
approved