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

Author

Antti Karttunen, Oct 20 2019

Keywords

• nonn
• base

Comments

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

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

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

Crossrefs

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

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

Cf. A227157 for analogous sequence.

Programs

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 *)

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));

Extensions

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