A167186 Record gaps between nonprime prime powers.

3, 4, 7, 9, 17, 40, 41, 74, 151, 307, 312, 408, 424, 912, 1032, 1217, 1872, 2518, 3713, 4920, 5208, 8400, 8520, 8892, 9297, 12840, 16008, 21840, 24360, 35880, 38808, 80760, 102168, 129480, 167160, 183960, 201072, 258720, 290760, 301242, 358848, 375468, 415920

Offset: 1

Author

Michael B. Porter, Oct 29 2009, Oct 31 2009, Nov 03 2009

Keywords

• nonn

Examples

			17 is in the sequence since A025475(9) - A025475(8) = 49 - 32 = 17, and no previous gap is larger.
A025475(10) - A025475(9) = 64 - 49 = 15, but the previous gap is larger, so 15 is not in the sequence.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..200

Crossrefs

List of nonprime prime powers: A025475.

Gaps between nonprime prime powers: A053707.

Record gaps between prime powers including primes: A121492.

Programs

Mathematica

Join[{3},DeleteDuplicates[Differences[Select[Range[10^6],PrimePowerQ[#] && !PrimeQ[ #]&]], GreaterEqual]] (* Harvey P. Dale, Feb 28 2023 *)

PARI

isA025475(n) = (omega(n) == 1 & !isprime(n)) || (n == 1)
d_max=0;n_prev=1;for(n=2,32e6,if(isA025475(n),d=n-n_prev;n_prev=n;if(d>d_max,print(d);d_max=d)))