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 A332848 Primes p such that (3*p+q)/2, (p+3*q)/2, (3*q+r)/2 and (q+3*r)/2 are all prime, where q and r are the next primes after p. 1
 809, 15331, 51071, 59183, 59447, 95747, 125737, 224069, 442733, 471677, 521869, 579757, 651517, 658873, 659453, 696989, 890887, 893449, 1035707, 1114193, 1236517, 1271807, 1299041, 1337593, 1435201, 1585513, 1590383, 1672271, 1707073, 1708363, 1817131, 1835003, 1963309, 1992527, 2078371, 2329597 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first of two consecutive primes that are both in A329151. The first case where a(n+1) is the next prime after a(n), i.e. a(n) and the next two primes are all in A329151, is a(176)=35103361. LINKS Robert Israel, Table of n, a(n) for n = 1..2000 EXAMPLE a(3) = 51071 is in the sequence because p=51071, q=51109, r=51131 are consecutive primes such that (3*p+q)/2=102161, (p+3*q)/2=102199, (3*q+r)/2=102229, (q+3*r)/2=102251 are all prime. MAPLE q:= 3: r:= 5: count:= 0: Res:= NULL: while count < 100 do p:= q; q:= r; r:= nextprime(q); if isprime((3*p+q)/2) and isprime((p+3*q)/2) and isprime((3*q+r)/2) and isprime((q+3*r)/2) then count:= count+1; Res:= Res, p; fi od: Res; MATHEMATICA Select[Partition[Prime[Range[175000]], 3, 1], AllTrue[{(3#[[1]]+#[[2]])/2, (#[[1]]+ 3#[[2]])/2, (3#[[2]]+#[[3]])/2, (#[[2]]+3#[[3]])/2}, PrimeQ]&][[;; , 1]] (* Harvey P. Dale, Mar 19 2023 *) CROSSREFS Cf. A329151. Sequence in context: A252028 A031599 A265984 * A160561 A346716 A156404 Adjacent sequences: A332845 A332846 A332847 * A332849 A332850 A332851 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Feb 26 2020 STATUS approved

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Last modified September 16 22:04 EDT 2024. Contains 375979 sequences. (Running on oeis4.)