A220697 Least prime in a string of exactly n consecutive primes all differing by semiprimes.

2, 7, 19, 43, 109, 151, 2341, 937, 9343, 25633, 62467, 125659, 634223, 696481, 36787867, 160729363, 186611561, 2687549003, 35217744131, 3961140077, 52556322253, 114326649397, 348705174313, 15234953708851, 163229981102789, 87255058923913

Offset

1,1

Comments

a(27) > 6*10^14. - Giovanni Resta, Jun 14 2013

Links

Table of n, a(n) for n=1..26.

Carlos Rivera, Puzzle 692 - Consecutive prime gaps biprimes, The Prime Puzzles & Problems Connection.

Example

The fifth entry is 109 because it is the least prime to begin a string of primes 109, 113, 127, 131, 137 having four semiprimes as differences between the consecutive primes: the consecutive semiprime differences are 4, 14, 4, 6.

Prog

(PARI) issemi(n)=bigomega(n)==2
back(p, n)=for(i=1, n, p=precprime(p-1)); p
r=t=1; v=vector(100); v[1]=p=2; forprime(q=3, 1e11, if(issemi(q-p), t++, if(t>=r && v[t]==0, v[t]=back(p, t-1); print(t" "v[t]); while(v[r], r++)); t=1); p=q) \\ Charles R Greathouse IV, Mar 01 2018

Crossrefs

Cf. A226768, A226769, A226840.

Sequence in context: A100119 A322385 A350170 * A078842 A110299 A209400

Adjacent sequences: A220694 A220695 A220696 * A220698 A220699 A220700

Keyword

nonn

Author

J. M. Bergot and Charles R Greathouse IV, Apr 25 2013

Extensions

a(16)-a(23) from Donovan Johnson, Apr 28 2013

a(24)-a(26) from Giovanni Resta, Jun 14 2013

Status

approved