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

%I A280773 #9 Jan 18 2017 21:11:20
%S A280773 3,5,11,23,31,73,79,83,109,127,139,181,191,193,197,199,211,241,227,
%T A280773 229,233,239,251,257,271,263,269,277,281,293
%N A280773 Primes p such that A280864(k) = 5p for some k yet A280864(k+1) != 6p.
%C A280773 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.
%C A280773 The present sequence lists the exceptions in the case Q=5.  It is quite likely that there are no further terms.
%C A280773 If Q=3, it appears that there are just five exceptions, 3, 11, 31, 59, 71.
%C A280773 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.
%C A280773 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.
%C A280773 All four of these searches were carried out using the first 100000 terms of A280864.
%e A280773 A280864(42) = 55 = 5*11, yet A280864(43) = 33 (not 66), so 11 is a term.
%e A280773 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).
%Y A280773 Cf. A280964.
%K A280773 nonn
%O A280773 1,1
%A A280773 _N. J. A. Sloane_, Jan 18 2017