0,3

Conjecture: To locate the next number, we need to find consecutive 1354 composite numbers, that is a prime gap (=difference of consecutive primes) of at least 1355. This starts at the prime 401429925999153707 (see Nicely link) and this generates a(5)=4014...707+1354=401429925999155061. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 27 2007

a(4) computed by Carlos Rivera, solutions of puzzle 141 by Chris Nash, Jud McCranie, Key Toshihara, Chu Lai, Felice Russo and Motua Guang.

M. T. Marcos, Smarandache Prime Base representation, prime puzzle 141.

Thomas R. Nicely, First occurrence prime gaps

a(n) = 2*p(m) - p(m-1) with minimal m = pi(a(n)) so that p(m) = a(n-1) + p(m-1).

a(3) = 23+3+1 = p(9)+p(2)+p(0) is the first n with 3 ones in 1000000101 = A007924(27).

p(n) = A008578(n), A007924 (binary Smarandache Prime Base representation).

Sequence in context: A066842 A133032 A110763 this_sequence A051674 A132641 A008973

Adjacent sequences: A066349 A066350 A066351 this_sequence A066353 A066354 A066355

more,nonn

Copied from www.primepuzzles.net by frank.ellermann(AT)t-online.de, Dec 19 2001.

The next term is > 4.29E17. It occurs where there is a gap of at least 1354 between two consecutive primes. - Randall L. Rathbun (randallr(AT)abac.com), Jan 27 2002

Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009