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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

With Bachet-Bezout 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*A024899-A034936)-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

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)