|
%I #14 Nov 30 2019 07:13:32
%S 1,2,3,5,8,9,14,15,20,24,35,80,125,224,384,440,539,714,1715,2079,2400,
%T 3024,4374,9800,12375,123200,194480,633555
%N 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.
%C The smallest prime in the set of consecutive primes is always 2, since k*(k+1) is even.
%C No further terms thru 5*10^8. - _Ray Chandler_, Jun 24 2009
%C a(29) > 2.29*10^25, if it exists. - _Giovanni Resta_, Nov 30 2019
%e 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.
%p 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
%Y Cf. A073491.
%K more,nonn
%O 1,2
%A _Leroy Quet_, Aug 03 2008
%E More terms from _Emeric Deutsch_, Aug 12 2008
|
