A340218 a(n) is the number of k < n such that prime(n)*prime(n+1) mod prime(k)*prime(k+1) is prime.

0, 1, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 3, 6, 1, 2, 5, 5, 3, 3, 4, 4, 4, 3, 6, 6, 6, 4, 9, 7, 4, 2, 8, 4, 5, 4, 4, 10, 4, 4, 10, 6, 3, 7, 4, 4, 7, 8, 4, 10, 6, 6, 9, 7, 3, 8, 7, 6, 9, 6, 7, 8, 11, 7, 4, 7, 9, 9, 9, 6, 5, 13, 4, 6, 7, 6, 5, 13, 8, 9, 11, 9, 7, 14, 12, 9, 7, 15, 10, 17, 10, 9, 13, 10

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 2 because prime(3)*prime(4) = 5*7 = 35, and 35 mod (2*3) = 5 and 35 mod (3*5) = 5 are prime.

Maple

N:= 100: # for a(1)..a(N)
P:= [seq(ithprime(i), i=1..N+1)]:
PP:= [seq(P[i]*P[i+1], i=1..N)]:
f:= proc(n) nops(select(t -> isprime(PP[n] mod PP[t]), [$1..n-1])) end proc:
map(f, [$1..N]);

Prog

(PARI) a(n) = sum(k=1, n-1, isprime(lift(Mod(prime(n)*prime(n+1), prime(k)*prime(k+1))))); \\ Michel Marcus, Jan 04 2021

Crossrefs

Cf. A006094.

Sequence in context: A205689 A050206 A127237 * A199968 A066482 A324507

Adjacent sequences: A340215 A340216 A340217 * A340219 A340220 A340221

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 03 2021

Status

approved