A383473 -id:A383473 - cp's OEIS frontend

A383475 Numbers k such that k*2^d is the average of a twin prime pair for some divisor d of k.

2, 3, 6, 9, 12, 15, 18, 21, 24, 30, 36, 39, 42, 45, 48, 51, 54, 60, 69, 72, 75, 78, 81, 90, 96, 99, 105, 108, 114, 120, 129, 132, 135, 141, 144, 150, 156, 165, 168, 174, 180, 186, 192, 201, 210, 216, 228, 231, 234, 240, 252, 258, 261, 264, 270, 282, 285, 288, 300

Offset: 1

Juri-Stepan Gerasimov, Apr 27 2025

nonn

			2 is a term in the sequence because 2*2^1 = 4 is the average of twin primes 3 and 5 for divisor d = 1 of k = 2.

Supersequence of 3*A002822 and 3*A060212.

Cf. A014574, A027750, A382811, A383473.

[k: k in [1..300] | not #[d: d in Divisors(k) | IsPrime(k*2^d-1) and IsPrime(k*2^d+1)] eq 0];

q[k_] := AnyTrue[Divisors[k], And @@ PrimeQ[k * 2^# + {-1, 1}] &]; Select[Range[300], q] (* Amiram Eldar, Apr 28 2025 *)

isok(k) = fordiv(k, d, if (isprime(k*2^d-1) && isprime(k*2^d+1), return(1))); return(0); \\ Michel Marcus, Apr 28 2025

A383836 Integers k such that d*2^k + k/d is prime for some divisor d of k.

Original entry on oeis.org

1, 3, 5, 6, 9, 10, 15, 21, 22, 28, 39, 66, 75, 81, 89, 105, 108, 111, 141, 165, 166, 190, 196, 317, 340, 357, 459, 462, 483, 525, 564, 568, 573, 701, 735, 737, 792, 869, 1185, 1311, 1480, 1647, 1794, 1881, 2145, 2405, 2508, 2766, 3081, 3201, 3225, 3243, 4260, 4713, 5369, 5795, 5985

Offset: 1

Juri-Stepan Gerasimov, May 11 2025

nonn

			6 is a term because 2*2^6 + 6/2 = 131 is prime for divisor d = 2 of k = 6.

Supersequence of A057663.

Cf. A161904, A383473.

[k: k in [1..1000] | not #[d: d in Divisors(k) | IsPrime(d*2^k+(k div d))] eq 0];

Select[Range[4300],Sum[Boole[PrimeQ[d*2^#+#/d]],{d,Divisors[#]}]>0 &] (* Stefano Spezia, May 16 2025 *)

is(n, f=factor(n))=fordiv(n>>valuation(n,2),d, if(isprime(n/d*2^n+d), return(1))); 0 \\ Charles R Greathouse IV, May 17 2025

a(41) corrected by Sean A. Irvine, May 21 2025

cp's OEIS Frontend

A383475 Numbers k such that k*2^d is the average of a twin prime pair for some divisor d of k.

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