A038347 -id:A038347 - cp's OEIS frontend

A078586 a(n) is the product of the first n primes of the form 4k+3.

3, 21, 231, 4389, 100947, 3129357, 134562351, 6324430497, 373141399323, 25000473754641, 1775033636579511, 140227657289781369, 11638895555051853627, 1198806242170340923581, 128272267912226478823167, 16290578024852762810542209, 2134065721255711928181029379

Offset: 1

T. D. Noe, Dec 01 2002

a(n)+2 is a prime for n=1,2,3,4,8,10,12,17,19,22,23,53.

Product of first n primes that are also Gaussian primes; product of first n primes that are not of the form x^2+y^2.

T. D. Noe, Table of n, a(n) for n = 1..100

Cf. A002110, A006278, A038347.

Partial products of A002145.

maxN=15; pLst={}; k=0; While[Length[pLst]

a(n)=my(t=1); forprime(p=2,,if(p%4==3, t*=p; if(n--<1,return(t)))) \\ Charles R Greathouse IV, Mar 09 2014

A038346 Sum of first n primes of form 4k+1.

Original entry on oeis.org

5, 18, 35, 64, 101, 142, 195, 256, 329, 418, 515, 616, 725, 838, 975, 1124, 1281, 1454, 1635, 1828, 2025, 2254, 2487, 2728, 2985, 3254, 3531, 3812, 4105, 4418, 4735, 5072, 5421, 5774, 6147, 6536, 6933

Offset: 1

Den Roussel (DenRoussel(AT)webtv.net)

Jianing Song, Table of n, a(n) for n = 1..10001

Cf. A002144, A002313, A006278, A038347.

Accumulate[Select[Prime[Range[100]],IntegerQ[(#-1)/4]&]] (* Harvey P. Dale, Jul 25 2011 *)

a(n) = my(s=0); forprime(p=2, , if(p%4==1, s+=p; if(n--<1, return(s)))) \\ following Charles R Greathouse IV's program for A078586

a(n) = Sum_{k=1..n} A002144(k). - Michel Marcus, Oct 18 2021

Offset corrected by Jianing Song, Oct 18 2021

cp's OEIS Frontend

A078586 a(n) is the product of the first n primes of the form 4k+3.

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