A167236 Larger prime power associated with gaps in A121492.

2, 7, 16, 23, 37, 59, 97, 149, 211, 307, 907, 1151, 1361, 5623, 8501, 9587, 15727, 19661, 31469, 156007, 360749, 370373, 492227, 1349651, 1357333, 2010881, 4652507, 17051887, 20831533, 47326913, 122164969, 189695893, 191913031, 387096383, 436273291, 1294268779

Offset: 1

Author

Michael B. Porter, Nov 01 2009, Nov 03 2009

Keywords

• nonn

Examples

			59 is in the sequence since 53 and 59 are consecutive prime powers with a difference of 6 and no smaller pair of consecutive prime powers differ by 6 or more.
		

Links

• Jan Kristian Haugland, Table of n, a(n) for n = 1..87. The extra terms after a(33) are copied from A000101 as the associated prime gaps do not contain any prime powers.

Crossrefs

Size of gap: A121492

Smaller prime power (start of gap): A002540

Gaps between prime powers: A057820

List of prime powers: A000961

Programs

PARI

isA000961(n) = (omega(n) == 1 || n == 1)
d_max=0;n_prev=1;for(n=2,1e6,if(isA000961(n),d=n-n_prev;if(d>d_max,print(n);d_max=d);n_prev=n))

Extensions

a(34) onwards from Jan Kristian Haugland, Oct 18 2024