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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.
2
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
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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Apr 26 2017
EXTENSIONS
a(24)-a(32) from Giovanni Resta, Apr 26 2017
STATUS
approved