A203018 The n-th prime number that equals 1 (mod 4n).

5, 41, 61, 193, 241, 337, 449, 673, 613, 1201, 1453, 1249, 2081, 2633, 1861, 3457, 4217, 3169, 6841, 4801, 4201, 7481, 9109, 6529, 7901, 13001, 8209, 12097, 12413, 8641, 16741, 17921, 10429, 19993, 15401, 16417, 24421, 26297, 17317, 23201, 33457, 21169

Offset: 1

Author

Zak Seidov, Dec 27 2011

Keywords

• nonn

Examples

			a(1)=5 because 1+4=5 is 1st prime == 1 mod 4,
a(2)=41 because 1+(4*2)*{2,5}={17,41} are 1st and 2nd primes == 1 mod 8,
a(3)=61 because 1+(4*3)*{1,3,5}={13,37,61} are 1st, 2nd and 3rd primes == 1 mod 12;
a(1000)=24952001=1+4000*6238;
a(10000)=3345120001=1+40000*83628;
a(10^5)=411686400001=A000040(16018223727)=1+4*10^6*1029216;
a(10^6)=48792928000001=A000040(1600641618847)=1+4*10^6*12198232.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A002144, A070848.