A185934 Lesser of two consecutive primes which both equal 1 (mod 3).

31, 61, 73, 151, 157, 199, 211, 271, 331, 367, 373, 433, 523, 541, 571, 601, 607, 619, 661, 727, 733, 751, 991, 997, 1033, 1063, 1069, 1117, 1123, 1201, 1231, 1237, 1291, 1321, 1381, 1453, 1459, 1531, 1543, 1621, 1657, 1669, 1741, 1747, 1753, 1759, 1777, 1789, 1861, 1987, 2011, 2131, 2161, 2179, 2281, 2287, 2341, 2371

Offset: 1

Author

M. F. Hasler, Feb 06 2011

Keywords

• nonn

Comments

Or, primes of the form 6k+1 such that the next prime is again of the form 6k'+1.

Examples

			The smallest prime of the form 6k+1 such that the next larger prime differs by a multiple of 3 (and thus a multiple of 6), is a(1) = 31, the following prime being 31+6 = 37.
Note that the next larger prime may also differ by 12 (as is the case for 199,211,619,661,997,1201,1237,1459,1531,1789,3049,...), or by 18 (as it is the case for 523,1069,1381,1759,2161,2503,3889,...), etc.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002476, A151800, A217659, A219244.

Programs

Haskell

a185934 n = a185934_list !! (n-1)
a185934_list = map (a000040 . (+ 1)) $
   elemIndices 1 $ zipWith (*) a039701_list $ tail a039701_list
-- Reinhard Zumkeller, Nov 16 2012

Mathematica

With[{p = Prime[Range[350]]}, ind = Position[Mod[p, 3], 1] // Flatten; p[[ind[[Position[Differences[ind], 1] // Flatten]]]]] (* Amiram Eldar, Apr 12 2025 *)

PARI

forprime( p=1,1e4, (o+0-o=p)%3==0 & o%3==1 & print1( precprime(p-1)","))

Formula

a(n) = A217659(n) - 6*A219244(n); A217659(n) = A151800(a(n)). - Reinhard Zumkeller, Nov 16 2012