A083273 a(n) is the quotient of lcm of first n consecutive prime differences and A001223(n), the n-th difference between consecutive primes.

1, 1, 1, 1, 2, 1, 2, 1, 2, 6, 2, 3, 6, 3, 2, 2, 6, 2, 3, 6, 2, 3, 2, 3, 6, 12, 6, 12, 6, 12, 42, 28, 84, 84, 420, 140, 140, 210, 140, 140, 420, 84, 420, 210, 420, 70, 70, 210, 420, 210, 140, 420, 84, 140, 140, 140, 420, 140, 210, 420, 84, 60, 210, 420, 210, 60, 140, 84, 420, 210

Offset: 1

Author

Labos Elemer, May 15 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A001223, A080374, A080375, A080376.

Programs

Mathematica

ld[x_] := Apply[LCM, Table[Prime[w+1]-Prime[w], {w, 1, x}]]; Table[ld[j]/(Prime[j+1]-Prime[j]), {j, 1, 100}]
seq[len_] := Module[{d = Differences[Prime[Range[len+1]]]}, FoldList[LCM, d]/d]; seq[70] (* Amiram Eldar, Feb 08 2025 *)

Formula

a(n) = A080374(n)/A001223(n).