A247969 a(n) is the smallest k such that prime(k+i) (mod 6) takes successively the values 1,5,1,5,... for i = 0, 1,...,n-1 ending with 1 or 5.

4, 4, 4, 4, 4, 4, 25, 25, 59, 141, 141, 141, 141, 141, 141, 141, 141, 141, 141, 141, 280230, 280230, 981960, 981960, 981960, 4505195, 4505195, 7438440, 15658002, 15658002, 15658002, 15658002, 2628111621, 4671618380, 4671618380, 5803722576, 5803722576, 5803722576

Offset: 1

Author

Michel Lagneau, Sep 28 2014

Keywords

• nonn

Examples

			a(1)= 4 => prime(4) (mod 6)= 1, and not for k = 1, 2, 3.
a(2)= 4 => prime(4) (mod 6)= 1, prime(5) (mod 6) = 5;
a(3)= 4 => prime(4) (mod 6)= 1, prime(5) (mod 6)= 5, prime(6) (mod 6)= 1.
The corresponding primes are for
n= 6: 7, 11, 13, 17, 19, 23;
n= 8: 97, 101, 103, 107, 109, 113, 127, 131;
n= 9: 277, 281, 283, 293, 307, 311, 313, 317, 331;
n= 20: 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941. - _Michel Marcus_, Sep 29 2014
		

Links

• Rémy Sigrist, PARI program for A247969

Crossrefs

Cf. A000040, A247816, A247967.

Programs

Maple

for n from 1 to 21 do :
ii:=0:
   for k from 3 to 10^5 while (ii=0)do :
     s:=0:
      for i from 0 to n-1 do:
        r:=irem(ithprime(k+i),6):
        if r = irem(5^i,6)
        then
        s:=s+1:
        else
        fi:
      od:
       if s=n and ii=0
       then
       printf ( "%d %d \n",n,k):ii:=1:
       else
       fi:
    od:
od:

PARI

a(n) = {k = 1; ok = 0; while (! ok, m = 1; nb = 0; for (i=0, n-1, if ((prime(k+i) % 6) == m, nb++, break); m = 5*m % 6;); if (nb == n, ok = 1, k++);); k;} \\ Michel Marcus, Sep 29 2014

PARI

See Links section.

Extensions

More terms from Rémy Sigrist, Oct 18 2020