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 A173177 Numbers n such that 2n+3 is a prime of the form 3*A034936+4. 1

%I

%S 2,5,8,14,17,20,29,32,35,38,47,50,53,62,68,74,77,80,89,95,98,104,110,

%T 113,119,134,137,140,152,155,164,167,173,182,185,188,197,203,209,215,

%U 218,227,230,242,248,260,269,272,284,287,299

%N Numbers n such that 2n+3 is a prime of the form 3*A034936+4.

%C With Bachet-Bezout theorem implicating Gauss Lemma

%C and the Fundamental Theorem of Arithmetic,

%C for n>1 n = 2*a+3*b (a and b integers)

%C first type

%C A001477 = (2* A080425 ) + (3* A008611)

%C A000040 = (2* A039701 ) + (3* A157966)

%C . A024893 Numbers n such that 3*n + 2 is prime

%C . A034936 Numbers n such that 3*n + 4 is prime

%C OR

%C second type

%C A001477 = (2* A028242 ) + (3* A059841)

%C A000040 = (2* A067076 ) + (3* 1 )

%C . A067076 Numbers n such that 2*n + 3 is prime

%C .n a b OR a b

%C .0 0 0 0 0

%C .1 - - - -

%C .2 1 0 1 0

%C .3 0 1 0 1

%C .4 2 0 2 0

%C .5 1 1 1 1

%C .6 0 2 3 0

%C .7 2 1 2 1

%C .8 1 2 4 0

%C .9 0 3 3 1

%C .10 2 2 5 0

%C .11 1 3 4 1

%C .12 0 4 6 0

%C .13 2 3 5 1

%C .14 1 4 7 0

%C .15 0 5 6 1

%C .. . . . .

%C .. . . . .

%C . 2* 2 +3 OR 3* 1 +4 = 7

%C . 2* 5 +3 3* 3 +4 = 13

%C . 2* 8 +3 3* 5 +4 = 19

%C . 2* 14 +3 3* 9 +4 = 31

%C . 2* 17 +3 3* 11 +4 = 37

%C . 2* 20 +3 3* 13 +4 = 43

%C . 2* 29 +3 3* 19 +4 = 61

%C . 2* 32 +3 3* 21 +4 = 67

%C . 2* 35 +3 3* 23 +4 = 73

%C A034936 Numbers n such that 3n+4 is prime.

%C A002476 Primes of form 6n+1.

%C A024899 Nonnegative integers n such that 6n+1 is prime.

%C 2,5,8,14,17,20...=(3*(4*A024899-A034936)-5)/2

%H Prime FAQ Chris K.Caldwell, <a href="http://primes.utm.edu/notes/faq/six.html">Most rediscovered result about primes numbers</a>

%t Select[Range[300],PrimeQ[2#+3]&&Divisible[2#-1,3]&] (* _Harvey P. Dale_, Aug 25 2016 *)

%Y Cf. A067076, A034936, A002476, A024899.

%K nonn

%O 1,1

%A _Eric Desbiaux_, Feb 11 2010

%E More terms from _Harvey P. Dale_, Aug 25 2016

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)