A328574 a(1) = 0, and, for n >= 2, numbers n whose primorial base expansion doesn't contain any nonleading zeros.

0, 1, 3, 5, 9, 11, 15, 17, 21, 23, 27, 29, 39, 41, 45, 47, 51, 53, 57, 59, 69, 71, 75, 77, 81, 83, 87, 89, 99, 101, 105, 107, 111, 113, 117, 119, 129, 131, 135, 137, 141, 143, 147, 149, 159, 161, 165, 167, 171, 173, 177, 179, 189, 191, 195, 197, 201, 203, 207, 209, 249, 251, 255, 257, 261, 263, 267, 269, 279, 281, 285

Offset

1,3

Comments

After the initial zero, numbers k for which A276086(k) produces an even number with no gaps in its prime factorization.

Numbers k such that A276086(k) is in A055932; numbers k for which A328475(k) is equal to A328572(k) = A003557(A276086(k)).

The number of positive terms below prime(m)# = A002110(m) is Sum_{k=1..m} A005867(k). - Amiram Eldar, Feb 16 2021

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base

Formula

{k such that A235224(k) = A267263(k)}. - Antti Karttunen, Feb 04 2026

Mathematica

max = 4; bases = Prime @ Range[max, 1, -1]; nmax = Times @@ bases - 1; Join[{0}, Select[Range[nmax], FreeQ[IntegerDigits[#, MixedRadix[bases]], 0] &]] (* Amiram Eldar, Feb 16 2021 *)

Prog

(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA055932(n) = { my(f=factor(n)[, 1]~); f==primes(#f); }; \\ From A055932
isA328574(n) = isA055932(A276086(n));
(PARI)
A328475(n) = { my(m=1, p=2, y=1); while(n, if(n%p, m *= p^((n%p)-y), y=0); n = n\p; p = nextprime(1+p)); (m); };
A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
isA328574(n) = (A328475(n) == A328572(n));

Crossrefs

Cf. A002110, A003557, A005867, A055932, A276086, A328475, A328572.

Positions of 1's in A328573, positions of 0's in A329027, cf. also A328840.

After the initial 0, gives positions of nonzero terms in A355037.

Positions where A235224 and A267263 are equal.

Subsequences: A143293, A341433, A392614, A392864.

Cf. A227157 for analogous sequence.

Sequence in context: A285519 A047270 A084060 * A227157 A024896 A160771

Adjacent sequences: A328571 A328572 A328573 * A328575 A328576 A328577

Keyword

nonn,base

Author

Antti Karttunen, Oct 20 2019

Extensions

Primary definition changed, the old definition moved to comment section by Antti Karttunen, Nov 03 2019

Status

approved