A381630 a(n) is the least k such that the sum of k and the k-th number with n prime factors (counted with multiplicity) has n prime factors (counted with multiplicity).

1, 4, 8, 14, 16, 16, 96, 80, 304, 448, 640, 1984, 544, 2048, 3584, 20480, 9216, 49152, 65536, 524288, 1245184, 3309568, 204800, 1179648, 28311552, 2426880, 29360128, 6291456, 27787264, 125829120, 67108864, 327155712, 1073741824

Offset: 1

Author

Robert Israel, Mar 07 2025

Keywords

• nonn
• more

Examples

			a(3) = 8 because the 8th number with 3 prime factors (the 8th triprime) is 42 = 2*3*7, 8 + 42 = 50 = 2 * 5^2 also has 3 prime factors, and 8 is the smallest number that works.
		

Crossrefs

Cf. A001222, A064402, A100915.

Programs

Maple

f:= proc(n) uses priqueue; local pq,k,t,i,q;
    initialize(pq);
    insert([-2^n,2$n],pq);
    for k from 1 do
       t:= extract(pq);
       if numtheory:-bigomega(k-t[1])=n then return k fi;
       q:= nextprime(t[-1]);
       for i from 1 to n while t[-i] = t[-1] do
         insert([t[1]*(q/t[-1])^i,op(t[2..n+1-i]),q$i],pq);
       od
    od
end proc:
map(f, [$1..30]); # Robert Israel, Mar 07 2025

Extensions

a(32) from Jinyuan Wang, Mar 09 2025

a(33) from Jinyuan Wang, Mar 21 2025