A190478 a(n) is the smallest prime prime(k) > a(n-1) such that the n numbers 2*prime(j)+3, j=k to k+n-1, are all prime.

2, 5, 13, 3767, 19913, 726109, 4827859, 59069473, 179993463679, 2280987436223

Offset

1,1

Comments

This essentially searches for blocks of n consecutive primes of the form A023204 (see also A089530) with a minimum of the primes in the block set by the previous entry in the sequence. - R. J. Mathar, Jun 02 2011

Any further terms are > 10^13. - Lucas A. Brown, Mar 17 2024

Links

Table of n, a(n) for n=1..10.

Lucas A. Brown, Python program.

Example

For n=1, 2 is prime and 2*2+3=7 is prime so a(1)=2.
For n=2, 5,7 are consecutive primes 2*5+3 and 2*7+3 are primes so a(2)=5 as 5 is the least such prime > 2.
For n=3, 13,17,19 are consecutive primes 2*13+3, 2*17+3, 2*19+3 are primes so a(3)=13 as 13 is the least such prime > 5.

Maple

isA023204 := proc(n) isprime(n) and isprime(2*n+3) ; end proc:
A190478idx := proc(n) option remember; if n = 1 then 1; else for a from procname(n-1)+1 do krun := true; for k from a to a+n-1 do if not isA023204(ithprime(k)) then krun := false; break; end if; end do: if krun then return a; end if; end do: end if; end proc:
A190478 := proc(n) ithprime( A190478idx(n)) ; end proc: # R. J. Mathar, Jun 02 2011

Prog

(PARI) old(p, k)=while(k--, p=precprime(p-1)); p;
n=1; k=0; forprime(p=2, 4e9, if(isprime(p<<1+3), if(k++==n, print1(old(p, n)", "); k--; n++), k=0)) \\ Charles R Greathouse IV, May 11 2011

Crossrefs

Cf. A023204.

Sequence in context: A196273 A128772 A272106 * A155838 A166405 A226505

Adjacent sequences: A190475 A190476 A190477 * A190479 A190480 A190481

Keyword

nonn,more,hard

Author

Pierre CAMI, May 11 2011

Extensions

a(8) from Charles R Greathouse IV, May 11 2011

a(9)-a(10) from Lucas A. Brown, Mar 17 2024

Status

approved