cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A307818 Numbers k such that A240718(k) = 0.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 12, 15, 19, 49, 61, 63, 64, 110, 151, 154, 166, 173, 244, 278, 427, 454, 481, 496, 572, 575, 637, 677, 680, 681, 691, 704, 712, 766, 884, 928, 964, 1039, 1094, 1100, 1219, 1256, 1265, 1309, 1321, 1729, 1909, 1924, 2309, 2443, 2686, 2989, 3001, 3004, 3713, 4798, 4801, 5134, 5311, 5719, 5821, 6443, 6574, 6781, 7099, 7339, 8251, 9454, 10684, 11416, 11713, 11728, 21766, 27122, 31637
Offset: 1

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Author

Robert Israel, Apr 30 2019

Keywords

Comments

k is in the sequence if there are no primes p < sqrt(2*k-2) such that 2*k-p is prime.
There are no other terms < 10^7.
Conjecture: 31637 is the last term.

Examples

			a(7)=9 is in the sequence because the primes < sqrt(2*9-2)=4 are 2 and 3, and neither 2*9-2=16 nor 2*9-3=15 is prime.
		

Crossrefs

Cf. A240718.

Programs

  • Maple
    P:= NULL: Res:= 1:  nextp:= 2:
    for n from 2 to 10^6 do
      while nextp^2 < 2*n-2 do
       P:= P, nextp;
       nextp:= nextprime(nextp);
      od;
      if andmap(t -> not isprime(2*n-t), [P]) then
       Res:= Res, n
      fi;
    od:
    Res;
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