OFFSET
1,1
COMMENTS
Weakening the definition to prime(k+i) == 2 (mod 3) yields a(1) = 1, but all other terms are unchanged. See also A247816 (residue 5) or A276414 (equal residues, all 1 or all -1). - M. F. Hasler, Sep 02 2016
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..35
FORMULA
a(n) = primepi(A057622(n)). - Michel Marcus, Oct 01 2014
EXAMPLE
a(1)= 3 => prime(3) == 5 (mod 6).
a(2)= 9 => prime(9) == 5 (mod 6), prime(10) == 5 (mod 6).
a(3)= 15 => prime(15) == 5 (mod 6), prime(16) == 5 (mod 6), prime(17) == 5 (mod 6).
From Michel Marcus, Sep 30 2014: (Start)
The resulting primes are:
5;
23, 29;
47, 53, 59;
251, 257, 263, 269;
1889, 1901, 1907, 1913, 1931;
7793, 7817, 7823, 7829, 7841, 7853;
43451, 43457, 43481, 43487, 43499, 43517, 43541;
243161, 243167, 243197, 243203, 243209, 243227, 243233, 243239;
... (End)
MAPLE
for n from 1 to 22 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 = 5
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:
MATHEMATICA
Table[k = 1; While[Times @@ Boole@ Map[Mod[Prime[k + #], 6] == 5 &, Range[0, n - 1]] == 0, k++]; k, {n, 10}] (* Michael De Vlieger, Sep 02 2016 *)
PROG
(PARI) a(n) = {k = 1; ok = 0; while (!ok, nb = 0; for (i=0, n-1, if (prime(k+i) % 6 == 5, nb++, break); ); if (nb == n, ok=1, k++); ); k; } \\ Michel Marcus, Sep 28 2014
(PARI) m=c=i=0; forprime(p=1, , i++; p%6!=5&&(!c||!c=0)&&next; c++>m||next; print1(1+i-m=c, ", ")) \\ M. F. Hasler, Sep 02 2016
(MATLAB)
N = 2*10^8; % to use primes up to N
P = mod(primes(N), 6);
P5 = find(P==5);
n5 = numel(P5);
a(1) = P5(1);
for k = 2:100
r = find(P5(k:n5) == P5(1:n5+1-k)+k-1, 1, 'first');
if numel(r) == 0
break
end
a(k) = P5(r);
end
a % Robert Israel, Sep 02 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 28 2014
EXTENSIONS
a(11)-a(22) from A057622 by Michel Marcus, Oct 03 2014
a(23)-a(25) from Jinyuan Wang, Jul 08 2019
a(26)-a(30) added using A057622 by Jinyuan Wang, Apr 15 2020
STATUS
approved