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A074927 a(n) such that p(n)*p(n+1)+a(n) is a minimal square. 5
3, 1, 1, 4, 1, 4, 1, 4, 9, 1, 9, 4, 1, 4, 9, 9, 1, 9, 4, 1, 9, 4, 9, 16, 4, 1, 4, 1, 4, 49, 4, 9, 1, 25, 1, 9, 9, 4, 9, 9, 1, 25, 1, 4, 1, 36, 36, 4, 1, 4, 9, 1, 25, 9, 9, 9, 1, 9, 4, 1, 25, 49, 4, 1, 4, 49, 9, 25, 1, 4, 9, 16, 9, 9, 4, 9, 16, 4, 16, 25, 1, 25, 1, 9, 4, 9, 16, 4, 1, 4, 36, 16, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

When a(n)=1, p(n) and p(n+1) are twin primes.

a(n+1) = A072681(A024675(n)). - Reinhard Zumkeller, Mar 04 2009

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

FORMULA

For n>1: a(n) = ((p(n+1)-p(n))/2)^2. - Reinhard Zumkeller, Oct 22 2002

EXAMPLE

a(154) = 100 because p(154)*p(155) + 100 = 804609 = 897^2.

MATHEMATICA

Flatten[{3, Table[((Prime[n+1]-Prime[n])/2)^2, {n, 2, 100}]}] (* Vaclav Kotesovec, Mar 23 2014 *)

Join[{3}, ((#[[2]]-#[[1]])/2)^2&/@Partition[Prime[Range[2, 100]], 2, 1]] (* Harvey P. Dale, Dec 04 2016 *)

CROSSREFS

Sequence in context: A104610 A138684 A132442 * A139605 A191780 A098712

Adjacent sequences:  A074924 A074925 A074926 * A074928 A074929 A074930

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 02 2002

STATUS

approved

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Last modified November 25 14:47 EST 2020. Contains 338625 sequences. (Running on oeis4.)