A090870 a(n) is the smallest m such that d(m+k-1) = 2k for k = 1, ..., n where d(t)= prime(t+1) - prime(t) (differences of consecutive primes in arithmetic progression).

2, 3, 7, 69, 1642, 12073, 12073, 6496152, 118033638, 5575956036, 165534366186, 3265469041280, 14779996741980, 5701362336480884

Offset: 1

Author

Farideh Firoozbakht, Dec 11 2003

Keywords

• nonn
• more

Comments

Is this sequence infinite?

Examples

			a(8) = 6496152 because prime(6496152) = 113575727 and 113575727, 113575729, 113575733, 113575739, 113575747, 113575757, 113575769, 113575783, and 113575799 are nine consecutive primes with differences respectively 2, 4, 6, 8, 10, 12, 14, 16.
		

Crossrefs

Cf. A016045, A049232.

Programs

Mathematica

a[n_] := (For[m=1, !Sum[(d[m+k-1]-2k)^2, {k, n}]==0, m++ ];m); Do[Print[a[n]], {n, 8}]

Formula

a(n) = primePi(A016045(n)).

Extensions

Extended and edited by T. D. Noe, May 23 2011

a(11)-a(14) from Amiram Eldar, Sep 06 2024