A093931 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.

3, 7, 11, 5, 19, 13, 17, 23, 29, 43, 37, 31, 41, 47, 53, 59, 73, 67, 61, 71, 97, 83, 79, 89, 103, 107, 101, 127, 113, 109, 131, 137, 151, 157, 163, 149, 139, 173, 167, 181, 191, 197, 193, 179, 241, 227, 223, 229, 233, 199, 257, 211, 269, 263, 277, 239, 313, 251

Offset

1,1

Comments

Is it true that every odd prime appears?

Links

Table of n, a(n) for n=1..58.

Example

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

Crossrefs

Cf. A000040, A065091, A100484.

Sequence in context: A229596 A125255 A125254 * A335980 A153788 A167486

Adjacent sequences: A093928 A093929 A093930 * A093932 A093933 A093934

Keyword

less,nonn

Author

Amarnath Murthy, Apr 25 2004

Extensions

a(14)-a(20) from Jonathan Vos Post, Mar 20 2006

More terms from David Wasserman, Mar 07 2007

Status

approved