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 A328822 Primes of the form p=3*q+3*r+q*r where q and r are distinct primes and 2*p-3*q, 2*p-3*r and 2*p-q*r are also prime. 2
 103, 151, 439, 503, 727, 751, 887, 1063, 1091, 1223, 1447, 1951, 2791, 2903, 3079, 3191, 3371, 3491, 3851, 4567, 5051, 5431, 5591, 5647, 6151, 6491, 7591, 9463, 9623, 11171, 12911, 14891, 15511, 16183, 17203, 18787, 19031, 19403, 19991, 20231, 21863, 22111, 22391, 22567, 24251, 24407, 26951 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The first term that occurs for more than one pair (q,r) is a(11)=1447, which corresponds to (q,r) = (5, 179) and (11, 101). The first term that occurs for more than two pairs (q,r) is a(2579)=15108791, which corresponds to (q,r) = (17, 755437), (37, 377717), and (2797, 5393). LINKS Robert Israel, Table of n, a(n) for n = 1..6030 EXAMPLE a(3)=439 is in the sequence because q=5 and r=53 are distinct primes with 439=3*q+3*r+q*r and 439, 2*439-3*q=863, 2*439-3*r=719 and 2*439-q*r=613 are all primes. MAPLE N:= 10^5: # to get all terms <= N Primes:= select(isprime, [seq(i, i=3..nextprime(N/8), 2)]): filter:= proc(p, q, r) isprime(p*q+2*p*r+2*q*r) and isprime(2*p*q+p*r+2*q*r) and isprime(2*p*q+2*p*r+q*r) end proc: p:= 3: R:= {}: for iq from 2 do q:= Primes[iq]; if 2*p*q + q^2 >= N then break fi; for ir from iq+1 do r:= Primes[ir]; s:= p*q + q*r + p*r; if s > N then break fi; if isprime(s) and filter(p, q, r) then R:= R union {s}; fi; od od: sort(convert(R, list)); MATHEMATICA M = 10^5; (* to get all terms <= M *) filterQ[p_, q_, r_] := PrimeQ[p q + 2 p r + 2 q r] && PrimeQ[2 p q + p r + 2 q r] && PrimeQ[2 p q + 2 p r + q r]; primes = Select[Table[i, {i, 3, NextPrime[M/8], 2}], PrimeQ]; p = 3; R = {}; For[iq = 2, True, iq++, q = primes[[iq]]; If[2 p q + q^2 >= M, Break[]]; For[ir = iq + 1, True, ir++, r = primes[[ir]]; s = p q + q r + p r; If[s > M, Break[]]; If[PrimeQ[s] && filterQ[p, q, r], R = Union[R, {s}]]]]; R (* Jean-François Alcover, Aug 12 2020, after Robert Israel *) CROSSREFS Primes in A328805. Sequence in context: A127027 A033256 A106983 * A141962 A309412 A115267 Adjacent sequences: A328819 A328820 A328821 * A328823 A328824 A328825 KEYWORD nonn AUTHOR Robert Israel, Oct 28 2019 STATUS approved

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Last modified September 19 04:19 EDT 2024. Contains 376004 sequences. (Running on oeis4.)