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A070043 Numbers of the form 6*j*k+j+k for positive integers j and k. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A274290 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

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Last modified February 25 11:50 EST 2018. Contains 299653 sequences. (Running on oeis4.)