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

1,1

Comments

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

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

Links

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

Example

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.

Prog

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

Crossrefs

Sequence in context: A228541 A115833 A189556 * A052158 A095672 A073650

Adjacent sequences: A185931 A185932 A185933 * A185935 A185936 A185937

Keyword

nonn

Author

M. F. Hasler, Feb 06 2011

Status

approved