cp's OEIS Frontend

A173177 Numbers k such that 2k+3 is a prime of the form 3*A034936(m) + 4.

%I A173177 #18 May 07 2025 12:36:29
%S A173177 2,5,8,14,17,20,29,32,35,38,47,50,53,62,68,74,77,80,89,95,98,104,110,
%T A173177 113,119,134,137,140,152,155,164,167,173,182,185,188,197,203,209,215,
%U A173177 218,227,230,242,248,260,269,272,284,287,299
%N A173177 Numbers k such that 2k+3 is a prime of the form 3*A034936(m) + 4.
%C A173177 With Bachet-Bézout theorem implicating Gauss Lemma and the Fundamental Theorem of Arithmetic,
%C A173177 for k > 1, k = 2*a + 3*b (a and b integers)
%C A173177 first type
%C A173177 A001477 = (2*A080425) + (3*A008611)
%C A173177 A000040 = (2*A039701) + (3*A157966)
%C A173177 A024893 Numbers k such that 3*k + 2 is prime
%C A173177 A034936 Numbers k such that 3*k + 4 is prime
%C A173177 OR
%C A173177 second type
%C A173177 A001477 = (2*A028242) + (3*A059841)
%C A173177 A000040 = (2*A067076) + (3*1)
%C A173177 A067076 Numbers k such that 2*k + 3 is prime
%C A173177    k   a b OR a b
%C A173177   --   - -    - -
%C A173177    0   0 0    0 0
%C A173177    1   - -    - -
%C A173177    2   1 0    1 0
%C A173177    3   0 1    0 1
%C A173177    4   2 0    2 0
%C A173177    5   1 1    1 1
%C A173177    6   0 2    3 0
%C A173177    7   2 1    2 1
%C A173177    8   1 2    4 0
%C A173177    9   0 3    3 1
%C A173177   10   2 2    5 0
%C A173177   11   1 3    4 1
%C A173177   12   0 4    6 0
%C A173177   13   2 3    5 1
%C A173177   14   1 4    7 0
%C A173177   15   0 5    6 1
%C A173177   ...
%C A173177   2* 2 + 3 OR 3* 1 + 4 =  7;
%C A173177   2* 5 + 3 OR 3* 3 + 4 = 13;
%C A173177   2* 8 + 3 OR 3* 5 + 4 = 19;
%C A173177   2*14 + 3 OR 3* 9 + 4 = 31;
%C A173177   2*17 + 3 OR 3*11 + 4 = 37;
%C A173177   2*20 + 3 OR 3*13 + 4 = 43;
%C A173177   2*29 + 3 OR 3*19 + 4 = 61;
%C A173177   2*32 + 3 OR 3*21 + 4 = 67;
%C A173177   2*35 + 3 OR 3*23 + 4 = 73.
%C A173177 A034936 Numbers k such that 3k+4 is prime.
%C A173177 A002476 Primes of the form 6k+1.
%C A173177 A024899 Nonnegative integers k such that 6k+1 is prime.
%C A173177 2, 5, 8, 14, 17, 20, ... = (3*(4*A024899 - A034936) - 5)/2.
%H A173177 Chris K. Caldwell, <a href="https://t5k.org/notes/faq/six.html">FAQ: Are all primes (past 2 and 3) of the forms 6n+1 and 6n-1?</a>
%t A173177 Select[Range[300],PrimeQ[2#+3]&&Divisible[2#-1,3]&] (* _Harvey P. Dale_, Aug 25 2016 *)
%Y A173177 Cf. A067076, A034936, A002476, A024899.
%K A173177 nonn,uned
%O A173177 1,1
%A A173177 _Eric Desbiaux_, Feb 11 2010
%E A173177 More terms from _Harvey P. Dale_, Aug 25 2016