A082098 - OEIS

%I #15 Feb 11 2025 01:20:19

%S 7,359,199,1831,887,2179,2971,5591,9551,33247,15683,106543,25471,

%T 153191,43331,288583,372539,360091,873787,542603,637939,544279,

%U 1291691,860143,1313467,1388483,2238823,2637799,6695747,1895359,6752623,3851459

%N a(n) is the smallest prime p of the form 4k+3 such that nextprime(p) - p = 4n.

%H Amiram Eldar, <a href="/A082098/b082098.txt">Table of n, a(n) for n = 1..100</a>

%e a(9) = 9551 since nextprime(9551) - 9551 = 9587 - 9551 = 36 = 4 * 9.

%t {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

%o (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

%Y Cf. A002144, A002145, A082073, A082074, A082075, A082076, A082099.

%K nonn

%O 1,1

%A _Labos Elemer_, Apr 14 2003