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A070848
Smallest prime == 1 mod (4n).
8
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
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, May 15 2002
EXTENSIONS
More terms from Benoit Cloitre, May 18 2002
STATUS
approved