A070848 Smallest prime == 1 mod (4n).

5, 17, 13, 17, 41, 73, 29, 97, 37, 41, 89, 97, 53, 113, 61, 193, 137, 73, 229, 241, 337, 89, 277, 97, 101, 313, 109, 113, 233, 241, 373, 257, 397, 137, 281, 433, 149, 457, 157, 641, 821, 337, 173, 353, 181, 1289, 941, 193, 197, 401, 409, 1249, 1061, 433, 661

Offset: 1

Author

Amarnath Murthy, May 15 2002

Keywords

• nonn

Comments

Note interesting patterns in the graph. - Zak Seidov, Dec 13 2011

Examples

			5 is the smallest prime of the form 1+4m, 17 is the smallest prime of the form 1+8m, 13 is the smallest prime of the form 1+12m, etc. - _Zak Seidov_, Dec 13 2011
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070846, A070847, A070849, A070850, A070851, A070852, A070853.

Cf. A034694.

Programs

Mathematica

nn=100; Reap[Do[p=1+4n; While[!PrimeQ[p], p=p+4n]; Sow[p], {n,nn}]][[2,1]] (* Zak Seidov, Dec 13 2011 *)

PARI

for(n=1,80,s=1; while((isprime(s)*s-1)%(4*n)>0,s++); print1(s,","))

PARI

nn=10000;for(n=1,nn,s=1+4*n;while(!isprime(s),s=s+4*n);print1(s,", ")) \\ Zak Seidov, Dec 13 2011

Python

from sympy import isprime
def a(n):
  k = 4*n + 1
  while not isprime(k): k += 4*n
  return k
print([a(n) for n in range(1, 56)]) # Michael S. Branicky, May 17 2021

Extensions

More terms from Benoit Cloitre, May 18 2002