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
Keywords
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
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 *)
Extensions
Corrected and extended by R. J. Mathar, Aug 06 2007
Data corrected by Amiram Eldar, Dec 30 2019
Comments