A280773 Primes p such that A280864(k) = 5p for some k yet A280864(k+1) != 6p.

3, 5, 11, 23, 31, 73, 79, 83, 109, 127, 139, 181, 191, 193, 197, 199, 211, 241, 227, 229, 233, 239, 251, 257, 271, 263, 269, 277, 281, 293

Offset: 1

Author

N. J. A. Sloane, Jan 18 2017

Keywords

• nonn

Comments

Let Q be a fixed odd prime. It appears that with only finitely many exceptions, when there is a term A280864(k) = Q*p, p prime, then the next term in A280864, A280864(k+1), is (Q+1)*p.

The present sequence lists the exceptions in the case Q=5. It is quite likely that there are no further terms.

If Q=3, it appears that there are just five exceptions, 3, 11, 31, 59, 71.

If Q=7, the complete list of exceptions appears to be 3, 5, 7, 11, 23, 37, 43, 73, 79, 83, 181, 191, 193, 197, 199, 211, 227, 229, 233, 239, 251, 257, 263, 269, 277, 1021, 1069, 1103, 1153.

If Q=11, the complete list of exceptions appears to be 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 47, 53, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 127, 139, 149, 151, 167, 173, 181, 191, 193, 197, 199, 211, 227, 229, 233, 239, 251, 257, 263, 269, 277, 281, 293, 311, 353, 431, 557, 563, 571, 619, 1289, 1291, 1307, 1499, 1571, 1579, 1583, 1621, 1627, 2011, 2029, 2131, 2207, 2221, 2281, 2287, 2311, 2341, 2347, 2357, 2399, 2551.

All four of these searches were carried out using the first 100000 terms of A280864.

Examples

			A280864(42) = 55 = 5*11, yet A280864(43) = 33 (not 66), so 11 is a term.
The more typical behavior is illustrated by A280864(52) = 65 = 5*13 and A280864(53) = 78 = 6*13 (and so 13 is not a term).
		

Crossrefs

Cf. A280964.