A328837 Numbers k for which A328403(k) = A276086(A276086(A276086(k))) is squarefree.

0, 1, 2, 4, 9, 2312

Offset: 1

Author

Antti Karttunen, Oct 30 2019

Keywords

• nonn
• hard
• more

Comments

Numbers k such that A276086(k) is in A328836, or equally, that A276087(k) is in A276156, i.e., numbers k for which A328828(A276087(k)) is zero, that is, numbers k such that in the primorial base expansion of A276087(k) there are no digits larger than 1.

All the terms of A328313 are also included in this sequence. Questions: Is that sequence finite? Even if it is, is this one also? Are there any terms here between 2312 and 3217644767340672907899084554132? Are there only finitely many numbers k for which A328828(A328403(k)) is zero? (See comments in A328398.)

Links

• Index entries for sequences related to primorial base

Crossrefs

Cf. A008966, A276086, A276087, A276156, A328313, A328403, A328828, A328836.

Positions of ones in A328394. See also comments in A328398.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328828(n) = { my(i=1, p=2); while(n, if((n%p)>1, return(i)); i++; n = n\p; p = nextprime(1+p)); (0); };
isA328837(n) = !A328828(A276086(A276086(n)));