A100395 The smallest prime number q such that the greatest prime divisor of 2*q+1 equals the n-th prime.
13, 2, 3, 5, 19, 59, 47, 11, 43, 139, 277, 61, 107, 23, 79, 29, 457, 167, 461, 109, 197, 41, 311, 727, 151, 257, 53, 163, 2203, 317, 1637, 479, 347, 223, 1283, 863, 733, 83, 1297, 89, 271, 859, 1061, 1871, 2089, 5591, 557, 113, 1259, 349, 1553, 3253, 1129, 2441
Offset: 2
Keywords
Examples
n=1: a(1)=13 because it is the least prime number such that the greatest prime divisor of 2*13 + 1 = 27 equals 3; n=2: a(2)=2 because the largest prime divisor of 2*a(2) + 1 = 5 is 5; n=6: a(6)=19 since the greatest prime factor of 2*19 + 1 = 39 = 3*13 is 13=prime(6).
Links
- Amiram Eldar, Table of n, a(n) for n = 2..10001
Programs
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Maple
A100395 := proc(n) p := ithprime(n) ; for i from 1 do q := ithprime(i) ; numtheory[factorset](2*q+1) ; if max(op(%)) = p then return q; end if; end do: end proc: seq(A100395(n),n=2..60) ; # R. J. Mathar, Sep 22 2018
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Mathematica
gpf[n_] := FactorInteger[n][[-1, 1]]; n = 54; m = Prime[n + 1]; v = Table[0, {m}]; c = 0; p = 2; While[c < n, g = gpf[2*p + 1]; If[g <= m && v[[g]] == 0, c++; v[[g]] = p]; p = NextPrime[p]]; Select[v, # > 0 &] (* Amiram Eldar, Aug 08 2020 *)
Formula
a(n) = Min{x; x is prime number; A006530(2x+1) = prime(n)}.
Comments