A099728 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.

380, 14, 5, 5, 365, 8, 5, 5, 14, 20, 5, 20, 8, 65, 8, 95, 35, 8, 14, 65, 20, 65, 8, 17, 350, 188, 5, 104, 98, 68, 35, 17, 158, 35, 92, 50, 62, 5, 26, 8, 8, 68, 233, 110, 5, 50, 23, 23, 8, 65, 59, 35, 14, 23, 35, 20, 47, 140, 5, 50, 14, 5, 44, 125, 386, 713, 23, 59, 44, 635, 98

Offset

1,1

Comments

Conjecture: No term is zero.

Links

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

Example

a(3) = 5 since A001359(3) = 11, 11 and 13 are twin primes, (11 - 5^2)^2 - 5 = 191, and 191 and 193 are also twin primes.

Maple

a135 := [] : f := fopen("b001359.txt", READ) : while nops(a135) < 200 do l := fscanf(f, "%d %d") : if l = [] then break : else a135 := [op(a135), l[2]] : fi ; od : for n from 1 to nops(a135) do a := op(n, a135) : B := 0 : while true do srch := (a-B^2)^2-B ; if isprime(srch) and isprime(srch+2) and srch > a then printf("%d, ", B) ; break ; fi ; B := B+1 : od : od: # R. J. Mathar, Aug 06 2007

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 *)

Crossrefs

Cf. A001359, A099742.

Sequence in context: A133962 A027503 A340200 * A206349 A252130 A252123

Adjacent sequences: A099725 A099726 A099727 * A099729 A099730 A099731

Keyword

nonn

Author

Ray G. Opao, Nov 07 2004

Extensions

Corrected and extended by R. J. Mathar, Aug 06 2007

Data corrected by Amiram Eldar, Dec 30 2019

Status

approved