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%I #15 Sep 06 2024 08:06:19
%S 2,3,7,69,1642,12073,12073,6496152,118033638,5575956036,165534366186,
%T 3265469041280,14779996741980,5701362336480884
%N 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).
%C Is this sequence infinite?
%F a(n) = primePi(A016045(n)).
%e 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.
%t a[n_] := (For[m=1, !Sum[(d[m+k-1]-2k)^2, {k, n}]==0, m++ ];m); Do[Print[a[n]], {n, 8}]
%Y Cf. A016045, A049232.
%K nonn,more
%O 1,1
%A _Farideh Firoozbakht_, Dec 11 2003
%E Extended and edited by _T. D. Noe_, May 23 2011
%E a(11)-a(14) from _Amiram Eldar_, Sep 06 2024