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 A347008 Numbers that can be written in exactly two ways as p*q+p+q where p and q are primes with p < q. 1
 23, 47, 119, 167, 179, 323, 407, 419, 527, 587, 639, 647, 879, 935, 1043, 1103, 1119, 1139, 1215, 1223, 1247, 1271, 1331, 1367, 1403, 1455, 1595, 1599, 1631, 1691, 1775, 1791, 1859, 1895, 1931, 1943, 1959, 1967, 1979, 2099, 2111, 2175, 2183, 2219, 2231, 2435, 2471, 2483, 2495, 2543, 2559, 2603 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..5000 EXAMPLE a(3) = 119 is a term because 119 = 5*19+5+19 = 3*29+3+29 are the two ways to produce 119 = p*q+p+q with primes p < q. MAPLE N:= 10000: # to produce terms <= N R:= Vector(N): P:= select(isprime, [2, seq(i, i=3..N/3, 2)]): for i from 1 to nops(P) do for j from 1 to i-1 do v:=P[i]*P[j]+P[i]+P[j]; if v <= N then R[v]:= R[v]+1 fi od od: select(t -> R[t]=2, [\$1..N]); PROG (Python) from sympy import primerange from collections import Counter def aupto(limit): primes = list(primerange(2, limit//3+1)) nums = [p*q+p+q for i, p in enumerate(primes) for q in primes[i+1:]] counts = Counter([k for k in nums if k <= limit]) return sorted(k for k in counts if counts[k] == 2) print(aupto(2604)) # Michael S. Branicky, Aug 10 2021 CROSSREFS Cf. A198277. Sequence in context: A043197 A043977 A042048 * A239563 A241207 A042050 Adjacent sequences: A347005 A347006 A347007 * A347009 A347010 A347011 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Aug 10 2021 STATUS approved

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Last modified November 29 09:49 EST 2022. Contains 358423 sequences. (Running on oeis4.)