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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).
0
2, 3, 7, 69, 1642, 12073, 12073, 6496152, 118033638, 5575956036, 165534366186, 3265469041280, 14779996741980, 5701362336480884
OFFSET
1,1
COMMENTS
Is this sequence infinite?
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
Sequence in context: A057736 A181263 A130309 * A088542 A075840 A096225
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