A175666 -id:A175666 - cp's OEIS frontend

A276626 Semiprimes n such that (n-1)/3 is prime.

10, 22, 34, 58, 94, 142, 178, 202, 214, 382, 394, 454, 502, 538, 634, 718, 922, 934, 1042, 1138, 1294, 1318, 1402, 1438, 1642, 1714, 1762, 1822, 1858, 1894, 1942, 2182, 2218, 2362, 2434, 2518, 2578, 2722, 2734, 2902, 2974, 3118, 3274, 3694, 3778, 3958, 4198, 4282, 4414, 4534, 4594, 4678

Offset: 1

Zak Seidov, Sep 07 2016

nonn

All semiprimes in A175666 are terms: a(2)=10=A175666(2), a(3)=34=A175666(4),etc.

			10=2*5 and (10-1)/3=3 prime, 22=2*11 and (22-1)/3=7 prime.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A175666.

Reap[Do[If[PrimeQ[(a=1+3*Prime[k])/2],Sow[a]],{k,1000}]][[2,1]]

isok(n) = (bigomega(n)==2) && (((n-1) % 3)==0) && isprime((n-1)/3); \\ Michel Marcus, Sep 07 2016

is(n)=n%3==1 && isprime(n\3) && bigomega(n)==2 \\ Charles R Greathouse IV, Sep 07 2016

A340509 a(n) = 3*A005382(n)-1.

Original entry on oeis.org

5, 8, 20, 56, 92, 110, 236, 290, 416, 470, 596, 632, 686, 812, 920, 992, 1010, 1100, 1136, 1316, 1496, 1640, 1730, 1802, 1820, 1856, 1982, 2072, 2180, 2432, 2486, 2630, 2810, 2900, 2990, 3026, 3206, 3512, 3710, 3836, 3890, 4196, 4286, 4376, 4592, 4826, 4880, 4970, 5276, 5600

Offset: 1

N. J. A. Sloane, Jan 27 2021, following a suggestion from Des MacHale

nonn

These are the numbers b(n) + 2*b(n)-1, where b is A005382, and so form a potentially infinite sequence of numbers which are the sum of two primes. An analog of A175666.

Cf. A005382, A005383, A005384, A175666.

q:= p-> isprime(2*p-1):
map(x-> 3*x-1, select(q, [ithprime(i)$i=1..300]))[]; # Alois P. Heinz, Jan 27 2021

Select[Range[5600], And @@ PrimeQ[{# + 1, 2*# - 1}/3] &] (* Amiram Eldar, Jan 27 2021 *)

a(n) = A005383(n) + A005382(n). - Wesley Ivan Hurt, Feb 22 2022

cp's OEIS Frontend

A276626 Semiprimes n such that (n-1)/3 is prime.

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