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A129809 Lesser of consecutive prime pairs whose last digits differ by 2. 1
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 (list; graph; refs; listen; history; text; internal format)
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
KEYWORD
easy,nonn,base
AUTHOR
Cino Hilliard, May 19 2007
STATUS
approved

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Last modified March 2 18:27 EST 2024. Contains 370498 sequences. (Running on oeis4.)