

A293619


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.


0



41, 941, 2269, 2411, 5101, 7193, 7283, 12011, 13159, 18427, 19183, 19961, 25589, 27751, 28579, 31151, 35771, 37313, 41543, 47087, 47939, 50459, 52691, 57251, 58229, 58897, 64279, 64553, 65827, 67121, 67411, 67741, 70853, 78277, 81869, 86353, 88993, 90007, 91253
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..39.


EXAMPLE

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.
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.
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.


MATHEMATICA

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]]


CROSSREFS

Cf. A000040, A292618, A292715, A292743, A293395.
Sequence in context: A282928 A114529 A300173 * A177418 A038397 A104349
Adjacent sequences: A293616 A293617 A293618 * A293620 A293621 A293622


KEYWORD

nonn


AUTHOR

K. D. Bajpai, Oct 13 2017


STATUS

approved



