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.

3, 2, 8, 17, 32, 97, 128, 257, 769, 2048, 4097, 6144, 8192, 40961, 73728, 65537, 131072, 524289, 524288, 3145728, 6291456, 8388608, 18874368, 50331648, 113246209, 167772161, 268435457, 805306368, 1610612737, 2147483649, 2147483648, 17179869184, 21474836480

Offset: 0

Author

Paolo P. Lava, Apr 26 2017

Keywords

• nonn

Comments

a(n) <= A051900(n), with equality for n=3,5,7,8,13,15. - Robert Israel, Apr 26 2017

Examples

			a(9) = 2048 because 2047 = 23 * 89, 2048 = 2^11 and 11 - 2 = 9.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A001222, A051900, A076191, A285457.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,k,v; v:=array(0..100);
for k from 0 to 100 do v[k]:=0; od; a:=0;
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;
while v[k]>0 do print(v[k]); k:=k+1; od; print(); end: P(10^6);

Mathematica

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 *)

Formula

Least solutions of the equation abs(A001222(k) - A001222(k-1)) = n.

Extensions

a(24)-a(32) from Giovanni Resta, Apr 26 2017