A324289 a(n) = A276086(A283477(n)).

2, 3, 5, 25, 7, 49, 117649, 184877, 11, 121, 1771561, 143, 36226650889, 59797108943, 546826709, 299019449675770681, 13, 169, 4826809, 23298085122481, 8254129, 68130645548641, 17750592470222918406076697669, 406193515012381653451063, 8223741426987700773289, 1553319630709265128413587, 1977089672816762887718980502697827

Offset: 0

Author

Antti Karttunen, Feb 23 2019

Keywords

• nonn

Comments

All primes are present, and furthermore, each subsequence starting at each n = 2^k is converging towards p^A283477(0), p^A283477(1), p^A283477(2), p^A283477(3), ..., where p = A000040(2+k). For example, for a(2^4) = a(16), the prime is A000040(2+4) = 13, and its powers 13^1, 13^2, 13^6 and 13^12 occur in successive positions from a(16) to a(19). See also comments in A324342.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..511
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base

Crossrefs

Cf. A000040, A001222, A276086, A283477, A324341, A324342.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A030308(n,k) = bittest(n,k);
A283477(n) = prod(i=0,#binary(n),if(0==A030308(n,i),1,A030308(n,i)*A002110(1+i)));
A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A324289(n) = A276086(A283477(n));

Formula

a(n) = A276086(A283477(n)).

For n >= 0, a(2^n) = A000040(2+n).

A001221(a(n)) = A324341(n).

A001222(a(n)) = A324342(n).