A082098 a(n) is the smallest prime p of the form 4k+3 such that nextprime(p) - p = 4n.
7, 359, 199, 1831, 887, 2179, 2971, 5591, 9551, 33247, 15683, 106543, 25471, 153191, 43331, 288583, 372539, 360091, 873787, 542603, 637939, 544279, 1291691, 860143, 1313467, 1388483, 2238823, 2637799, 6695747, 1895359, 6752623, 3851459
Offset: 1
Keywords
Examples
a(9) = 9551 since nextprime(9551) - 9551 = 9587 - 9551 = 36 = 4 * 9.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..100
Programs
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Mathematica
{m=4, r=3}; 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 == 3 && r2 == 3, 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