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A083552
Quotient when LCM of 2 consecutive prime differences is divided by GCD of the same two differences.
2
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, May 22 2003
STATUS
approved