A220697 - OEIS

%I #45 Nov 05 2023 09:02:38

%S 2,7,19,43,109,151,2341,937,9343,25633,62467,125659,634223,696481,

%T 36787867,160729363,186611561,2687549003,35217744131,3961140077,

%U 52556322253,114326649397,348705174313,15234953708851,163229981102789,87255058923913

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

%C a(27) > 6*10^14. - _Giovanni Resta_, Jun 14 2013

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_692.htm">Puzzle 692 - Consecutive prime gaps biprimes</a>, The Prime Puzzles & Problems Connection.

%e 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.

%o (PARI) issemi(n)=bigomega(n)==2

%o back(p,n)=for(i=1,n, p=precprime(p-1)); p

%o 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

%Y Cf. A226768, A226769, A226840.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Charles R Greathouse IV_, Apr 25 2013

%E a(16)-a(23) from _Donovan Johnson_, Apr 28 2013

%E a(24)-a(26) from _Giovanni Resta_, Jun 14 2013