A082099 a(n) is the smallest prime p of the form 4k+1 such that nextprime(p) - p = 4n.
13, 89, 509, 1933, 1637, 1669, 5953, 27701, 12853, 19333, 36389, 28229, 19609, 82073, 102701, 89689, 134513, 31397, 212701, 815729, 461717, 1155733, 927869, 360653, 396733, 3422813, 3279841, 370261, 5845193, 6085441, 6808273, 9810653
Offset: 1
Keywords
Examples
a(9) = 12853 since nextprime(12853) - 12853 = 12889 - 12853 = 36 = 4 * 9.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..100
Programs
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Mathematica
{m=4, r=1}; f[x_] := (Prime[x+1]-Prime[x])/m t=Table[0, {100}]; Do[s=f[n]; s1=Mod[Prime[n+1], m]; If[IntegerQ[s]&&Equal[s1, r]&&s<101&&t[[s]]==0, t[[s]]=Prime[n]], {n, 1, 1000000}]; t -
PARI
list(len) = {my(v = vector(len), c = 0, p1 = 2, r1 = p1 % 4, r2, i); forprime(p2 = 3, , r2 = p2 % 4; if(r1 == 1 && r2 == 1, i = (p2 - p1) / 4; if(i <= len && v[i] == 0, c++; v[i] = p1; if(c == len, break))); p1 = p2; r1 = r2); v;} \\ Amiram Eldar, Feb 11 2025