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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Cf. A034694.

Sequence in context: A356403 A178197 A302159 * A213738 A060829 A096896

Adjacent sequences: A070845 A070846 A070847 * A070849 A070850 A070851

Keyword

nonn

Author

Amarnath Murthy, May 15 2002

Extensions

More terms from Benoit Cloitre, May 18 2002

Status

approved