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%I #12 Nov 09 2017 14:05:56
%S 41,941,2269,2411,5101,7193,7283,12011,13159,18427,19183,19961,25589,
%T 27751,28579,31151,35771,37313,41543,47087,47939,50459,52691,57251,
%U 58229,58897,64279,64553,65827,67121,67411,67741,70853,78277,81869,86353,88993,90007,91253
%N Initial member of 6 consecutive primes a, b, c, d, e, f such that both (f + a)/(d - c) and (e + b)/(d - c) are prime.
%e 41 is a term because it is the smallest member of 6 consecutive primes {41, 43, 47, 53, 59, 61} = {a, b, c, d, e, f} and both (f + a)/(d - c) = 17 and (e + b)/(d - c) = 17 are prime.
%e 941 is a term because it is the smallest member of 6 consecutive primes {941, 947, 953, 967, 971, 977} = {a, b, c, d, e, f} and both (f + a)/(d - c) = 137 and (e + b)/(d - c) = 137 are prime.
%e 7193 is a term because it is the smallest member of 6 consecutive primes {7193, 7207, 7211, 7213, 7219, 7229} = {a, b, c, d, e, f} and both (f + a)/(d - c) = 7211 and (e + b)/(d - c) = 7213 are prime.
%t Select[Partition[Prime@Range[50000], 6, 1], Function[{a, b, c, d, e, f}, And[PrimeQ[(f + a)/(d - c)] && PrimeQ[(e + b)/(d - c)]]] @@ # &][[All, 1]]
%Y Cf. A000040, A292618, A292715, A292743, A293395.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Oct 13 2017
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