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
Keywords
Examples
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.
Links
- Carlos Rivera, Puzzle 692 - Consecutive prime gaps biprimes, The Prime Puzzles & Problems Connection.
Programs
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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
Extensions
a(16)-a(23) from Donovan Johnson, Apr 28 2013
a(24)-a(26) from Giovanni Resta, Jun 14 2013
Comments