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A285787 Least number k such that the absolute value of the difference between the number of prime factors, with multiplicity, of k and k-1 is equal to n.

%I A285787 #28 Apr 27 2017 05:49:34
%S A285787 3,2,8,17,32,97,128,257,769,2048,4097,6144,8192,40961,73728,65537,
%T A285787 131072,524289,524288,3145728,6291456,8388608,18874368,50331648,
%U A285787 113246209,167772161,268435457,805306368,1610612737,2147483649,2147483648,17179869184,21474836480
%N A285787 Least number k such that the absolute value of the difference between the number of prime factors, with multiplicity, of k and k-1 is equal to n.
%C A285787 a(n) <= A051900(n), with equality for n=3,5,7,8,13,15. - _Robert Israel_, Apr 26 2017
%H A285787 Giovanni Resta, <a href="/A285787/b285787.txt">Table of n, a(n) for n = 0..40</a>
%F A285787 Least solutions of the equation abs(A001222(k) - A001222(k-1)) = n.
%e A285787 a(9) = 2048 because 2047 = 23 * 89, 2048 = 2^11 and 11 - 2 = 9.
%p A285787 with(numtheory): P:=proc(q) local a,b,k,v; v:=array(0..100);
%p A285787 for k from 0 to 100 do v[k]:=0; od; a:=0;
%p A285787 for k from 2 to q do b:=bigomega(k); if v[abs(b-a)]=0 then v[abs(b-a)]:=k; fi; a:=b; od; k:=0;
%p A285787 while v[k]>0 do print(v[k]); k:=k+1; od; print(); end: P(10^6);
%t A285787 s = PrimeOmega@ Range[10^6]; 1 + First /@ Values@ KeySort@ PositionIndex@ Flatten@ Map[Abs@ Differences@ # &, Partition[s, 2, 1]] (* _Michael De Vlieger_, Apr 26 2017, Version 10 *)
%Y A285787 Cf. A001222, A051900, A076191, A285457.
%K A285787 nonn
%O A285787 0,1
%A A285787 _Paolo P. Lava_, Apr 26 2017
%E A285787 a(24)-a(32) from _Giovanni Resta_, Apr 26 2017