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

1,1

Comments

Is this sequence infinite?

Links

Table of n, a(n) for n=1..14.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A016045, A049232.

Sequence in context: A057736 A181263 A130309 * A088542 A075840 A096225

Adjacent sequences: A090867 A090868 A090869 * A090871 A090872 A090873

Keyword

nonn,more

Author

Farideh Firoozbakht, Dec 11 2003

Extensions

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

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

Status

approved