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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 21:28 EDT 2019. Contains 328244 sequences. (Running on oeis4.)