A141399 A positive integer k is included if all the distinct primes that divide k and k+1 together are members of a set of consecutive primes. In other words, k is included if and only if k*(k+1) is contained in sequence A073491.

1, 2, 3, 5, 8, 9, 14, 15, 20, 24, 35, 80, 125, 224, 384, 440, 539, 714, 1715, 2079, 2400, 3024, 4374, 9800, 12375, 123200, 194480, 633555

Offset

1,2

Comments

The smallest prime in the set of consecutive primes is always 2, since k*(k+1) is even.

No further terms thru 5*10^8. - Ray Chandler, Jun 24 2009

a(29) > 2.29*10^25, if it exists. - Giovanni Resta, Nov 30 2019

Links

Table of n, a(n) for n=1..28.

Example

20 is factored as 2^2 * 5^1. 21 is factored as 3^1 * 7^1. Since the distinct primes that divide 20 and 21 (which are 2,3,5,7) form a set of consecutive primes, then 20 is in the sequence.

Maple

with(numtheory): a:=proc(n) local F, m: F:=`union`(factorset(n), factorset(n+1)): m:=nops(F): if ithprime(m)=F[m] then n else end if end proc: seq(a(n), n=1..1000000); # Emeric Deutsch, Aug 12 2008

Crossrefs

Cf. A073491.

Sequence in context: A009388 A190803 A125871 * A104737 A286495 A295082

Adjacent sequences: A141396 A141397 A141398 * A141400 A141401 A141402

Keyword

more,nonn

Author

Leroy Quet, Aug 03 2008

Extensions

More terms from Emeric Deutsch, Aug 12 2008

Status

approved