A099742 Least number B such that (A001359(n)-B^2)^2+B is also the lesser of larger twin primes, or 0 if no such B exists.

1, 1, 1, 7, 412, 7, 7, 133, 7, 7, 316, 7, 25, 10, 10, 10, 7, 7, 16, 10, 7, 25, 1, 7, 7, 100, 55, 7, 28, 940, 37, 148, 22, 16, 28, 67, 31, 82, 64, 4, 82, 445, 292, 310, 16, 1687, 13, 37, 43, 7, 58, 22, 31, 97, 70, 7, 22, 1, 19, 52, 58, 25, 1, 367, 4, 7, 4, 37, 55

Offset: 1

Author

Ray G. Opao, Nov 09 2004

Keywords

• nonn

Comments

Conjecture: No term is zero.

Examples

			a(3) = 1 since A001359(3) = 11, 11 & 13 are twin primes, (11 - 1^2)^2 + 1 = 101, and 101 & 103 are also twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A099728.

Programs

Mathematica

f[p_] := Module[{b = 1}, While[(pb = (p - b^2)^2 + b) <= p || ! And @@ PrimeQ[pb + {0, 2}], b++]; b]; seq = {}; Do[If[And @@ PrimeQ[p + {0, 2}], AppendTo[seq, f[p]]], {p, 2, 3000}]; seq (* Amiram Eldar, Dec 30 2019 *)

Extensions

More terms from Amiram Eldar, Dec 30 2019