A343478 -id:A343478 - cp's OEIS frontend

A343480 Decimal expansion of 9 * Product_{p prime >= 5} (1-3/p)/(1-1/p)^3.

5, 7, 1, 6, 4, 9, 7, 1, 9, 1, 4, 3, 8, 4, 4, 0, 8, 6, 4, 8, 6, 0, 2, 6, 9, 3, 2, 1, 4, 5, 2, 7, 0, 1, 7, 5, 6, 0, 7, 8, 5, 9, 1, 1, 8, 5, 9, 9, 1, 3, 5, 2, 0, 5, 8, 0, 9, 7, 6, 1, 0, 1, 4, 4, 3, 8, 1, 0, 6, 1, 5, 1, 8, 0, 4, 5, 2, 5, 2, 6, 9, 3, 8, 7, 2, 2, 6

Offset: 1

Amiram Eldar, Apr 16 2021

This constant appears in the conjectured asymptotic formulas for A343478 and A343479.

			5.71649719143844086486026932145270175607859118599135...

Carlos Esparza and Lukas Gehring, Estimating the density of a set of primes with applications to group theory, arXiv:1810.08679 [math.NT], 2018.

Cf. A271886, A343478, A343479.

9 * prodeulerrat((1-3/p)/(1-1/p)^3, 1, 5)

Equals 2*A271886. - Hugo Pfoertner, Feb 11 2025

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).

Original entry on oeis.org

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

Offset: 1

Amiram Eldar, Apr 16 2021

nonn

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...

			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.

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.

Subsequence of A343478.

Cf. A003627, A038550, A215504, A343480.

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[2000], q]

cp's OEIS Frontend

A343480 Decimal expansion of 9 * Product_{p prime >= 5} (1-3/p)/(1-1/p)^3.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula