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A247970
a(n) is the smallest k such that prime(k+i) (mod 6) takes successively the values 5,1,5,1... for i = 0, 1,...,n-1 ending with 1 or 5.
0
3, 3, 3, 3, 3, 3, 3, 24, 24, 140, 140, 140, 140, 140, 140, 140, 140, 140, 140, 140, 140
OFFSET
1,1
COMMENTS
If a(22) exists, k > 10^5.
EXAMPLE
a(1)= 3 => prime(3) (mod 6)= 5;
a(2)= 3 => prime(3) (mod 6)= 5, prime(4) (mod 6) = 1;
a(3)= 3 => prime(3) (mod 6)= 5, prime(4) (mod 6)= 1, prime(5) (mod 6)= 5.
MAPLE
with(numtheory):
for n from 1 to 35 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+1), 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:
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Michel Lagneau, Sep 28 2014
STATUS
approved