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