

A173177


Numbers n such that 2n+3 is a prime of the form 3*A034936+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
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OFFSET

1,1


COMMENTS

With BachetBezout theorem implicating Gauss Lemma
and the Fundamental Theorem of Arithmetic,
for n>1 n = 2*a+3*b (a and b integers)
first type
A001477 = (2* A080425 ) + (3* A008611)
A000040 = (2* A039701 ) + (3* A157966)
. A024893 Numbers n such that 3*n + 2 is prime
. A034936 Numbers n such that 3*n + 4 is prime
OR
second type
A001477 = (2* A028242 ) + (3* A059841)
A000040 = (2* A067076 ) + (3* 1 )
. A067076 Numbers n such that 2*n + 3 is prime
.n 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 3* 3 +4 = 13
. 2* 8 +3 3* 5 +4 = 19
. 2* 14 +3 3* 9 +4 = 31
. 2* 17 +3 3* 11 +4 = 37
. 2* 20 +3 3* 13 +4 = 43
. 2* 29 +3 3* 19 +4 = 61
. 2* 32 +3 3* 21 +4 = 67
. 2* 35 +3 3* 23 +4 = 73
A034936 Numbers n such that 3n+4 is prime.
A002476 Primes of form 6n+1.
A024899 Nonnegative integers n such that 6n+1 is prime.
2,5,8,14,17,20...=(3*(4*A024899A034936)5)/2


LINKS

Table of n, a(n) for n=1..51.
Prime FAQ Chris K.Caldwell, Most rediscovered result about primes numbers


MATHEMATICA

Select[Range[300], PrimeQ[2#+3]&&Divisible[2#1, 3]&] (* Harvey P. Dale, Aug 25 2016 *)


CROSSREFS

Cf. A067076, A034936, A002476, A024899.
Sequence in context: A009203 A202273 A210702 * A191109 A190105 A295400
Adjacent sequences: A173174 A173175 A173176 * A173178 A173179 A173180


KEYWORD

nonn


AUTHOR

Eric Desbiaux, Feb 11 2010


EXTENSIONS

More terms from Harvey P. Dale, Aug 25 2016


STATUS

approved



