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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-B├ęzout 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

Table of n, a(n) for n=1..30.

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.)