A083552 Quotient when LCM of 2 consecutive prime differences is divided by GCD of the same two differences.

2, 1, 2, 2, 2, 2, 2, 6, 3, 3, 6, 2, 2, 6, 1, 3, 3, 6, 2, 3, 6, 6, 12, 2, 2, 2, 2, 2, 14, 14, 6, 3, 5, 5, 3, 1, 6, 6, 1, 3, 5, 5, 2, 2, 6, 1, 3, 2, 2, 6, 3, 5, 15, 1, 1, 3, 3, 6, 2, 5, 35, 14, 2, 2, 14, 21, 15, 5, 2, 6, 12, 12, 1, 6, 6, 12, 2, 2, 20, 5, 5, 5, 3, 6, 6, 12, 2, 2, 2, 3, 6, 2, 2, 2, 6, 2, 6, 9

Offset

1,1

Comments

Conjecture: Every positive integer appears infinitely many times in this sequence. Example: a(834) = a(909) = ... = a(9901) = ... = 4. - Jerzy R Borysowicz, Dec 22 2018

All terms of this sequence are integers because gcd(r,s) divides lcm(r,s) for any r and s. - Jerzy R Borysowicz, Jan 05 2019

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = lcm(A001223(n), A001223(n+1))/gcd(A001223(n), A001223(n+1));

a(n) = A083551(n)/A057467(n).

Mathematica

f[x_] := Prime[x+1]-Prime[x]; Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 1, 128}]

Prog

(PARI) a(n) = my(da=prime(n+2)-prime(n+1), db=prime(n+1)-prime(n)); lcm(da, db)/gcd(da, db) \\ Felix Fröhlich, Jan 05 2019

Crossrefs

Cf. A001223, A083538-A083555, A057467.

Sequence in context: A113793 A289499 A215904 * A326034 A332207 A339929

Adjacent sequences: A083549 A083550 A083551 * A083553 A083554 A083555

Keyword

nonn

Author

Labos Elemer, May 22 2003

Status

approved