A070043 Numbers of the form 6*j*k+j+k for positive integers j and k.

8, 15, 22, 28, 29, 36, 41, 43, 50, 54, 57, 60, 64, 67, 71, 78, 79, 80, 85, 92, 93, 98, 99, 104, 106, 113, 117, 119, 120, 127, 129, 132, 134, 136, 141, 145, 148, 154, 155, 158, 160, 162, 169, 171, 174, 176, 179, 183, 184, 190, 191, 193, 197, 204, 210, 211, 212

Offset

1,1

Comments

Equivalently, numbers r such that 6*r+1 has a nontrivial factor == 1 (mod 6).

These numbers, together with numbers of the form 6*j*k-j-k (A070799) are the numbers s for which 6*s+1 is composite (A046954). If we also add in the numbers of the form 6*j*k+j-k (A046953), we get the numbers t such that 6*t-1 and 6*t+1 do not form a pair of twin primes (A067611).

If N is the set of natural numbers, then the set N-{A070043 U A070799} are the numbers k that make 6*k+1 prime. - Pedro Caceres, Jan 22 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..9000

Example

41 = 6*2*3 + 2 + 3. Equivalently, 6*41+1 = (6*2+1)*(6*3+1).

Mathematica

Select[Range[250], MemberQ[Mod[Take[Divisors[6#+1], {2, -2}], 6], 1]&]

Crossrefs

Cf. A070799, A046953, A046954, A067611.

Sequence in context: A328410 A089025 A088977 * A003786 A008686 A003331

Adjacent sequences: A070040 A070041 A070042 * A070044 A070045 A070046

Keyword

nonn

Author

Jon Perry, May 05 2002

Extensions

Edited by Dean Hickerson and Vladeta Jovovic, May 07 2002

Status

approved