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

0,1

Comments

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A001222, A051900, A076191, A285457.

Sequence in context: A165660 A171634 A107300 * A047946 A066045 A110866

Adjacent sequences: A285784 A285785 A285786 * A285788 A285789 A285790

Keyword

nonn

Author

Paolo P. Lava, Apr 26 2017

Extensions

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

Status

approved