A083552 - OEIS

%I #46 Apr 09 2021 03:50:45

%S 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,

%T 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,

%U 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

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

%C 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

%C 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

%H Amiram Eldar, <a href="/A083552/b083552.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%o (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

%Y Cf. A001223, A083538-A083555, A057467.

%K nonn

%O 1,1

%A _Labos Elemer_, May 22 2003