A294075 a(n) is the distance from the n-th isolated prime number to the average of the next twin prime pair.

2, 7, 5, 13, 7, 5, 23, 19, 13, 5, 25, 11, 7, 23, 17, 13, 7, 17, 5, 7, 19, 13, 7, 5, 19, 5, 31, 17, 11, 67, 61, 53, 47, 41, 37, 31, 23, 19, 11, 23, 19, 13, 5, 55, 43, 35, 31, 23, 19, 13, 29, 23, 13, 7, 23, 13, 7, 11, 5, 11, 13, 7, 137, 133

Offset

1,1

Links

Table of n, a(n) for n=1..64.

Example

For n=2, the second isolated prime number is 23. The next twin prime pair after 23 is (29, 31). The average (29 + 31)/2 = 30. The difference 30 - 23 = 7 is the second term.

Mathematica

Block[{s = Prime@ Range@ 200, q, r}, q = Select[Partition[s, 2, 1], Differences@ # == {2} &]; r = Complement[s, Union@ Flatten@ q]; q = Mean /@ q; TakeWhile[#, IntegerQ] &@ Table[SelectFirst[q, # > p &] - p, {p, r}]] (* Michael De Vlieger, Feb 16 2018 *)

Prog

(PARI) {
  p=2; t1=2;
  forprime(t=3, 1000,
    if(t-p==2,
      t2=p+1;
      forprime(i=t1, t2-2,
        print1(t2-i, ", ")
      );
      t1=t2+2
    );
    p=t
  )
}
(PARI) lista(nn) = {forprime(p=2, nn, if(!isprime(p-2)&&!isprime(p+2), forprime(q = p+1, , if (isprime(q+2), print1(q+1-p, ", "); break); ); ); ); } \\ Michel Marcus, Mar 01 2018

Crossrefs

Cf. A007510, A014574.

Sequence in context: A135076 A155546 A073132 * A165355 A038004 A100792

Adjacent sequences: A294072 A294073 A294074 * A294076 A294077 A294078

Keyword

nonn

Author

Dimitris Valianatos, Feb 07 2018

Status

approved