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A174321 Index of the smallest prime greater than (6n+1)^2.

%I A174321 #19 Mar 06 2025 08:29:07
%S A174321 1,16,40,73,115,163,220,284,358,435,520,610,706,812,924,1039,1164,
%T A174321 1295,1424,1573,1716,1878,2033,2191,2367,2548,2730,2916,3108,3303,
%U A174321 3513,3732,3946,4165,4397,4628,4858,5107,5357,5612,5883,6148,6415,6685,6961,7253
%N A174321 Index of the smallest prime greater than (6n+1)^2.
%H A174321 Paolo Xausa, <a href="/A174321/b174321.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Robert Israel)
%F A174321 a(n) = A000720(A151800(A016922(n))). - _Michel Marcus_, Mar 06 2025
%e A174321 a(0)=1 because prime(1) > (6*0 + 1)^2;
%e A174321 a(1)=16 because prime(16) > (6*1+1)^2 > prime(15);
%e A174321 a(2)=40 because prime(40) > (6*2+1)^2 > prime(39).
%p A174321 A174321 := proc(n) numtheory[pi](nextprime((6*n+1)^2)) ; end proc: seq(A174321(n),n=0..80) ; # _R. J. Mathar_, Mar 29 2010
%t A174321 A174321[n_] := PrimePi[NextPrime[(6*n + 1)^2]]; Array[A174321, 50, 0] (* _Paolo Xausa_, Mar 06 2025 *)
%Y A174321 Cf. A000720, A151800, A016922.
%K A174321 nonn,easy
%O A174321 0,2
%A A174321 _Juri-Stepan Gerasimov_, Mar 15 2010
%E A174321 Definition corrected by _Charles R Greathouse IV_, Mar 20 2010
%E A174321 Offset corrected by _Robert Israel_, Mar 05 2025