A096475 a(n) is the smallest lesser of twin prime p, such that prime(2 + p) - prime(p) = 2n (cf. A096474).
3, 17, 11, 41, 71, 101, 29, 569, 881, 137, 1151, 521, 1289, 2027, 10331, 1229, 3461, 461, 2549, 2129, 6569, 6131, 14387, 34157, 5657, 4259, 44621, 17387, 25301, 11159, 56099, 34367, 64877, 23201, 80147, 73361, 21017, 46349, 162287, 94439, 469877, 122501, 35507
Offset: 3
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 3..202
Programs
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Mathematica
{ta = Table[0, {1300}], tb = Table[0, {1300}], tc = Table[0, {1300}], u = 1}; Do[s = Prime[n + 1] - Prime[n]; If[s == 2, ta[[u]] = Prime[Prime[n + 1]] - Prime[Prime[n]]; tb[[u]] = n; tc[[u]] = Prime[n]; u = u + 1], {n, 1, 10000}]; a[n_] := tc[[FirstPosition[ta, 2 n][[1]]]]; Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Jul 28 2017, using Mathematica code for A096464 *) -
PARI
a(n) = {forprime(p=3, , if (isprime(p+2) && (prime(2+p)-prime(p) == 2*n), return (p))); p=3;} \\ Michel Marcus, Jul 28 2017 -
PARI
list(len) = {my(v = vector(len), c = 0, q = 2, p1 = 2, p2 = 3, i); forprime(p3 = 5, , q++; if(isprime(q) && isprime(q-2), i = (p3-p1)/2 - 2; if(i <= len && v[i]==0, v[i] = q-2; c++; if(c == len, break))); p1 = p2; p2 = p3); v;} \\ Amiram Eldar, Feb 14 2025
Formula
a(n) = min{x; A096474(x) = 2n} for n = 3, 4, ...
Extensions
Name edited by Michel Marcus, Jul 28 2017
a(41)-a(45) from Michel Marcus, Jul 28 2017