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A173178 Numbers n such that 2n+3 is a prime of the form 3*A024893+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 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* 1 +3 OR 3* 1 +2 = 5

. 2* 4 +3 3* 3 +2 = 11

. 2* 7 +3 3* 5 +2 = 17

. 2* 10 +3 3* 7 +2 = 23

. 2* 13 +3 3* 9 +2 = 29

. 2* 19 +3 3* 13 +2 = 41

. 2* 22 +3 3* 15 +2 = 47

. 2* 25 +3 3* 17 +2 = 53

. 2* 28 +3 3* 19 +2 = 59

A024893 Numbers n such that 3n+2 is prime.

A007528 Primes of form 6n-1.

A024898 Positive integers n such that 6n-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: A276874 A310685 A310686 * A287555 A008470 A002640

Adjacent sequences:  A173175 A173176 A173177 * A173179 A173180 A173181

KEYWORD

nonn

AUTHOR

Eric Desbiaux, Feb 11 2010

STATUS

approved

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Last modified May 19 08:25 EDT 2019. Contains 323389 sequences. (Running on oeis4.)