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%I #8 Mar 31 2012 14:40:08
%S 2,3,7,69,1642,12073,12073,6496152,118033638,5575956036
%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 more,nonn
%O 1,1
%A _Farideh Firoozbakht_, Dec 11 2003
%E Extended and edited by _T. D. Noe_, May 23 2011
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