%I #13 Aug 27 2024 22:20:40
%S 3,7,11,5,19,13,17,23,29,43,37,31,41,47,53,59,73,67,61,71,97,83,79,89,
%T 103,107,101,127,113,109,131,137,151,157,163,149,139,173,167,181,191,
%U 197,193,179,241,227,223,229,233,199,257,211,269,263,277,239,313,251
%N a(1) = 3; for n>1, a(n) = smallest odd prime not already in the sequence such that a(n)-a(n-1) is twice a prime.
%C Is it true that every odd prime appears?
%e a(14) = Min{p such that p is in A000040 and a(n)-a(n+1) is in A100484 and not a(n+1) = a(k) for k <= n} = previously unused primes in S = 41 - {4, 6, 10, 14, 22, 26, 34, 38}. S = {3, 7, 15, 19, 27, 31, 35, 37}. Primes in S are {3, 7, 19, 31, 37}. But these are all terms equal or prior to a(13), hence we now seek the smallest prime p new to the sequence such that p - 41 is an even semiprime. S' = 41 + {A100484} = {45, 47, 51, 55, 63, 67, 75, 79, ...}. Primes in this are {47, 67, 79, ...} of which the minimum is a(14) = 47. - _Jonathan Vos Post_, Mar 20 2006
%Y Cf. A000040, A065091, A100484.
%K less,nonn
%O 1,1
%A _Amarnath Murthy_, Apr 25 2004
%E a(14)-a(20) from _Jonathan Vos Post_, Mar 20 2006
%E More terms from _David Wasserman_, Mar 07 2007