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

1,5

Links

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

Formula

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

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 *)

Crossrefs

Cf. A001223, A080374, A080375, A080376.

Sequence in context: A215745 A059913 A329602 * A353398 A193163 A106157

Adjacent sequences: A083270 A083271 A083272 * A083274 A083275 A083276

Keyword

nonn

Author

Labos Elemer, May 15 2003

Status

approved