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A173177
Numbers k such that 2k+3 is a prime of the form 3*A034936(m) + 4.
1
2, 5, 8, 14, 17, 20, 29, 32, 35, 38, 47, 50, 53, 62, 68, 74, 77, 80, 89, 95, 98, 104, 110, 113, 119, 134, 137, 140, 152, 155, 164, 167, 173, 182, 185, 188, 197, 203, 209, 215, 218, 227, 230, 242, 248, 260, 269, 272, 284, 287, 299
OFFSET
1,1
COMMENTS
With 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* 2 + 3 OR 3* 1 + 4 = 7;
2* 5 + 3 OR 3* 3 + 4 = 13;
2* 8 + 3 OR 3* 5 + 4 = 19;
2*14 + 3 OR 3* 9 + 4 = 31;
2*17 + 3 OR 3*11 + 4 = 37;
2*20 + 3 OR 3*13 + 4 = 43;
2*29 + 3 OR 3*19 + 4 = 61;
2*32 + 3 OR 3*21 + 4 = 67;
2*35 + 3 OR 3*23 + 4 = 73.
A034936 Numbers k such that 3k+4 is prime.
A002476 Primes of the form 6k+1.
A024899 Nonnegative integers k such that 6k+1 is prime.
2, 5, 8, 14, 17, 20, ... = (3*(4*A024899 - A034936) - 5)/2.
MATHEMATICA
Select[Range[300], PrimeQ[2#+3]&&Divisible[2#-1, 3]&] (* Harvey P. Dale, Aug 25 2016 *)
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Eric Desbiaux, Feb 11 2010
EXTENSIONS
More terms from Harvey P. Dale, Aug 25 2016
STATUS
approved