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A288209 Numbers n such that prime(n) * prime(n + 1) mod prime(n + 2) is odd. 0
1, 2, 5, 7, 10, 14, 15, 23, 29, 46, 61 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Finite? Full?

Next term, if it exists, is greater than 1026351685.

From Robert Israel, Jun 19 2017: (Start)

Numbers n such that floor(A001223(n+1)*A031131(n)/prime(n+2)) is odd.

Cramér's conjecture implies the sequence is finite. - Robert Israel, Jun 19 2017

LINKS

Table of n, a(n) for n=1..11.

Wikipedia, Cramér's conjecture

EXAMPLE

The first five primes are 2, 3, 5, 7, 11.

We see that 2 * 3 = 1 mod 5, so 1 (corresponding to the first prime, 2) is in the sequence.

We see that 3 * 5 = 1 mod 7, so 2 (corresponding to the second prime, 3) is in the sequence.

But 5 * 7 = 2 mod 11, so 3 (corresponding to the third prime, 5) is not in the sequence.

MAPLE

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):

select(n -> (P[n]*P[n+1] mod P[n+2])::odd, [$1..nops(P)-2]); # Robert Israel, Jun 19 2017

MATHEMATICA

Select[Range[1000], OddQ[Mod[Prime[#] Prime[# + 1], Prime[# + 2]]] &] (* Alonso del Arte, Jun 06 2017 *)

Position[Partition[Prime[Range[70]], 3, 1], _?(OddQ[Mod[#[[1]]#[[2]], #[[3]]]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Aug 11 2017 *)

PROG

(PARI) isok(n) = (((prime(n) * prime(n + 1)) % prime(n + 2)) % 2); \\ Michel Marcus, Jun 07 2017

CROSSREFS

Cf. A001223, A006094, A031131, A182126.

Sequence in context: A073593 A241510 A088947 * A071113 A071704 A267374

Adjacent sequences:  A288206 A288207 A288208 * A288210 A288211 A288212

KEYWORD

nonn

AUTHOR

Zak Seidov, Jun 06 2017

STATUS

approved

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Last modified October 19 23:44 EDT 2019. Contains 328244 sequences. (Running on oeis4.)