A129809 Lesser of consecutive prime pairs whose last digits differ by 2.

3, 5, 11, 17, 41, 71, 89, 101, 107, 137, 191, 197, 211, 227, 281, 311, 347, 359, 389, 431, 449, 461, 467, 479, 521, 523, 617, 641, 661, 683, 719, 743, 797, 821, 827, 857, 881, 929, 983, 997

Offset

1,1

Comments

Conjecture: The number of terms in this sequence is infinite.

This follows from Dickson's conjecture. - Charles R Greathouse IV, Jan 29 2013

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

I conjecture that a(n) ~ 4n log n. - Charles R Greathouse IV, Jan 29 2013

Example

The last digits of the consecutive prime pair 89 and 97 differ by 2 so 89 is in the table.

Mathematica

Select[Partition[Prime[Range[200]], 2, 1], Abs[Mod[#[[1]], 10]-Mod[#[[2]], 10]] == 2&][[All, 1]] (* Harvey P. Dale, Sep 14 2018 *)

Prog

(PARI) \d can be 2, 4, 6, 8 primediffd(n, d) = { forprime(x=3, n, y=abs((nextprime(x+1)%10-x%10)); if(y==d, print1(x", ") ) ) }
(PARI) p=2; forprime(q=3, 1e4, if(abs(q%10-p%10)==2, print1(p", ")); p=q) \\ Charles R Greathouse IV, Jan 29 2013

Crossrefs

Sequence in context: A252089 A128550 A096479 * A208572 A040176 A092873

Adjacent sequences: A129806 A129807 A129808 * A129810 A129811 A129812

Keyword

easy,nonn,base

Author

Cino Hilliard, May 19 2007

Status

approved