A084737 Beginning with 1, numbers such that (a(n+2)-a(n+1))/(a(n+1)-a(n)) = prime(n).

1, 2, 4, 10, 40, 250, 2560, 32590, 543100, 10242790, 233335660, 6703028890, 207263519020, 7628001653830, 311878265181040, 13394639596851070, 628284422185342480, 33217442899375387210, 1955977793053588026280

Offset

1,2

Comments

Successive differences are primorials.

Links

Table of n, a(n) for n=1..19.

Index entries for sequences related to primorial numbers

Formula

From Antti Karttunen, Feb 06 2024: (Start)

For n >= 1, a(n) = A276085(2*A002110(n-1)).

For n >= 2, a(n) = 1 + A143293(n-2).

For n >= 3, a(n) = 2 + A060389(n-2).

(End)

Example

a(3) = 4, a(4) = 10 and a(5) = 40 and (40-10)/(10-4) = 5 = prime(3).

Mathematica

Join[{1}, Accumulate[FoldList[Times, 1, Prime[Range[20]]]]+1] (* Harvey P. Dale, Dec 14 2011 *)

Crossrefs

Cf. A002110, A060389, A088860, A143293, A276085.

Sequence in context: A326904 A111022 A086852 * A322698 A153757 A159860

Adjacent sequences: A084734 A084735 A084736 * A084738 A084739 A084740

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 14 2003

Extensions

More terms from Vladeta Jovovic, Jun 17 2003

Status

approved