A083519 Beginning with 1, a(i)*a(j) + 2 is prime for all i, j, i != j.

1, 3, 5, 9, 129, 1179, 21105, 96525, 419925, 13690959, 8403613179

Offset

0,2

Comments

All terms are odd and equal to p - 2 for some prime p. Definition assumes that a(i+1) > a(i) as otherwise adding 1 to any initial subsequence would still satisfy the definition. - Chai Wah Wu, Jan 12 2019

For n >= 2, the last digit of a(n) is 5 or 9. - Pontus von Brömssen, Oct 12 2023

Links

Table of n, a(n) for n=0..10.

Example

1*3 + 2, 3*5 + 2, 1*5 + 2, etc. are primes.
9*1 + 2 = 11, 9*3 + 2 = 29, 9*5 + 2 = 47 are all primes, therefore a(4) = 9.

Mathematica

a = {1}; For[n = 2, n < 1000000, n++, b = Table[a[[i]]*n + 2, {i, 1, Length[ a]}]; If[Union[PrimeQ[b], PrimeQ[b]] == {True}, AppendTo[a, n]]]; a (* Stefan Steinerberger, Jun 02 2007 *)

Crossrefs

Cf. A083518.

Sequence in context: A098339 A121622 A188983 * A302088 A211414 A173706

Adjacent sequences: A083516 A083517 A083518 * A083520 A083521 A083522

Keyword

hard,more,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003

Extensions

Corrected and extended by Stefan Steinerberger, Jun 02 2007

a(10) from Donovan Johnson, Nov 11 2008

Status

approved