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 A173178 Numbers k such that 2k+3 is a prime of the form 3*A024893(m) + 2. 1
 0, 1, 4, 7, 10, 13, 19, 22, 25, 28, 34, 40, 43, 49, 52, 64, 67, 73, 82, 85, 88, 94, 97, 112, 115, 118, 124, 127, 130, 133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS With the Bachet-Bézout theorem implicating Gauss Lemma and the Fundamental Theorem of Arithmetic, for k > 1, k = 2*a + 3*b (a and b integers) first type A001477 = (2*A080425) + (3*A008611) A000040 = (2*A039701) + (3*A157966) A024893 Numbers k such that 3*k + 2 is prime A034936 Numbers k such that 3*k + 4 is prime OR second type A001477 = (2*A028242) + (3*A059841) A000040 = (2*A067076) + (3*1) A067076 Numbers k such that 2*k + 3 is prime    k   a b OR a b   --   - -    - -    0   0 0    0 0    1   - -    - -    2   1 0    1 0    3   0 1    0 1    4   2 0    2 0    5   1 1    1 1    6   0 2    3 0    7   2 1    2 1    8   1 2    4 0    9   0 3    3 1   10   2 2    5 0   11   1 3    4 1   12   0 4    6 0   13   2 3    5 1   14   1 4    7 0   15   0 5    6 1   ...   2* 1 + 3 OR 3* 1 + 2 =  5;   2* 4 + 3 OR 3* 3 + 2 = 11;   2* 7 + 3 OR 3* 5 + 2 = 17;   2*10 + 3 OR 3* 7 + 2 = 23;   2*13 + 3 OR 3* 9 + 2 = 29;   2*19 + 3 OR 3*13 + 2 = 41;   2*22 + 3 OR 3*15 + 2 = 47;   2*25 + 3 OR 3*17 + 2 = 53;   2*28 + 3 OR 3*19 + 2 = 59. A024893 Numbers k such that 3k+2 is prime. A007528 Primes of the form 6k-1. A024898 Positive integers k such that 6k-1 is prime. 1, 4, 7, 10, 13, 19, ... = (3*(4*A024898 - A024893) - 7)/2 = (A112774 - 3*A024893 - 5)/2 = A003627 - (3*A024893 - 5)/2. LINKS Prime FAQ Chris K.Caldwell, Most rediscovered result about primes numbers CROSSREFS Cf. A067076, A024893, A007528, A024898. Sequence in context: A310685 A310686 A339637 * A348156 A287555 A008470 Adjacent sequences:  A173175 A173176 A173177 * A173179 A173180 A173181 KEYWORD nonn,uned,more AUTHOR Eric Desbiaux, Feb 11 2010 STATUS approved

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Last modified August 10 16:24 EDT 2022. Contains 356039 sequences. (Running on oeis4.)