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 A343479 Prime numbers p == 2 (mod 3) such that p-1 has exactly one odd prime divisor and p+1 has exactly one prime divisor > 3 (counting prime divisors with multiplicity in both). 3
 29, 41, 59, 83, 89, 113, 137, 167, 173, 179, 227, 233, 263, 269, 317, 347, 353, 359, 467, 479, 503, 557, 563, 593, 641, 653, 719, 773, 809, 887, 977, 983, 1097, 1187, 1193, 1283, 1307, 1367, 1433, 1439, 1487, 1493, 1523, 1619, 1697, 1823, 1907, 1997, 2063, 2153 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Esparza and Gehring (2018) proved that assuming a generalized Hardy-Littlewood conjecture the number of terms not exceeding x is asymptotically (c/2) * x/log(x)^3, where c = A343480 = 5.716497... LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Carlos Esparza and Lukas Gehring, Estimating the density of a set of primes with applications to group theory, arXiv:1810.08679 [math.NT], 2018. EXAMPLE 29 is a term since it is prime, 29 = 3*9 + 2, 29-1 = 28 = 2^2 * 7 has only one odd prime divisor (7) and 29+1 = 30 = 2*3*5 has only one prime divisor (5) larger than 3. MATHEMATICA q[n_] := Mod[n, 3] == 2 && PrimeQ[n] && PrimeQ[(n + 1)/2^IntegerExponent[n + 1, 2]/3^IntegerExponent[n + 1, 3]] && PrimeQ[(n - 1)/2^IntegerExponent[n - 1, 2]]; Select[Range, q] CROSSREFS Subsequence of A343478. Cf. A003627, A038550, A215504, A343480. Sequence in context: A069454 A035789 A343478 * A080899 A216815 A157141 Adjacent sequences:  A343476 A343477 A343478 * A343480 A343481 A343482 KEYWORD nonn AUTHOR Amiram Eldar, Apr 16 2021 STATUS approved

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Last modified October 27 10:47 EDT 2021. Contains 348274 sequences. (Running on oeis4.)