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

Author

Pierre CAMI, May 11 2011

Keywords

• nonn
• more
• hard

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

Examples

			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.
		

Links

• Lucas A. Brown, Python program.

Crossrefs

Cf. A023204.

Programs

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

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

Extensions

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

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