A330771 Averages k of twin primes such that adding divisors of k to (k - 1, k + 1) produces record numbers of twin prime pairs.

4, 180, 6300, 65520, 282240, 2116800, 6652800, 31600800, 43076880, 226951200, 289578240, 300207600, 397837440, 940539600, 1470268800, 1574773200, 3602158560, 7618665600, 17459442000, 88735046400, 131675544000, 149232283200, 170075505600, 439977938400, 449755225920

Offset

1,1

Comments

Values of A014574 corresponding to records in A330768.

Record values corresponding to a(1)-a(34) are 1, 4, 5, 8, 10, 14, 18, 19, 22, 23, 26, 28, 31, 34, 37, 38, 44, 51, 65, 69, 72, 80, 88, 89, 96, 98, 102, 120, 125, 137, 151, 181, 219, 236.

Links

Giovanni Resta, Table of n, a(n) for n = 1..34

Example

a(3) = 6300 is in the sequence because A014574(148) = 6300, A330768(148) = 5, and A330768(n) < 5 for n < 148.

Maple

f:= proc(n)
    nops(select(t -> isprime(n+t) and isprime(n+2+t), numtheory:-divisors(n+1)))
end proc:
R:= 4: count:= 1: rcount:= 1: vmax:= 1:
for k from 5 by 6 while count < 50000 do
  if isprime(k) and isprime(k+2) then
    count:= count+1; v:=f(k);
    if v > vmax then
      R:= R, k+1;
      rcount:= rcount+1;
      vmax:= v;
    fi
  fi
od:R;

Crossrefs

Cf. A014574, A330768.

Sequence in context: A300387 A082393 A176351 * A263436 A269195 A269102

Adjacent sequences: A330768 A330769 A330770 * A330772 A330773 A330774

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 30 2019

Extensions

a(10) and beyond from Giovanni Resta, Jan 03 2020

Status

approved