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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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: A133961 A133962 A027503 * 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

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)