login
A220697
Least prime in a string of exactly n consecutive primes all differing by semiprimes.
3
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(16)-a(23) from Donovan Johnson, Apr 28 2013
a(24)-a(26) from Giovanni Resta, Jun 14 2013
STATUS
approved