A035791 Start of a string of exactly 3 consecutive (but disjoint) pairs of twin primes.

5, 179, 809, 3359, 4217, 6761, 18041, 21587, 26861, 49367, 67187, 80447, 82721, 91127, 97841, 98897, 103967, 109829, 122597, 154157, 178037, 203321, 208931, 225749, 227609, 236867, 243671, 251201, 266447, 285611, 289109, 295871, 317729

Offset: 1

Author

Randall L Rathbun

Keywords

• nonn
• easy

Examples

			a(2)=179 because (179,181),(191,193),(197,199) is the second occurrence (after (5,7),(11,13),(17,19)) of exactly 3 pairs of twin primes.
		

References

• Posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Nov. 19 1998.

Links

• Sebastian Petzelberger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A035789, A035790, A035792, A035793, A035794, A035795, A087641.

Programs

Mathematica

Select[Prime@ Range@ 30000, And[ NextPrime[#, -1] - NextPrime[#, -2] != 2, NextPrime@ # - # == 2, NextPrime[#, 3] - NextPrime[#, 2] == 2, NextPrime[#, 5] - NextPrime[#, 4] == 2, NextPrime[#, 7] - NextPrime[#, 6] > 2] &] (* Michael De Vlieger, Apr 25 2015 *)
Select[Partition[Prime[Range[30000]],10,1],#[[8]]-#[[7]]==#[[6]]-#[[5]] == #[[4]] - #[[3]]==2&&#[[2]]-#[[1]]!=2&&#[[10]]-#[[9]]!=2&][[All,3]] (* Harvey P. Dale, Mar 14 2018 *)

Extensions

More terms from Hugo Pfoertner, Sep 05 2003

Offset corrected by Arkadiusz Wesolowski, May 06 2012