A363242 Numbers whose primorial-base representation contains only odd digits.

1, 3, 9, 21, 39, 51, 99, 111, 159, 171, 249, 261, 309, 321, 369, 381, 669, 681, 729, 741, 789, 801, 1089, 1101, 1149, 1161, 1209, 1221, 1509, 1521, 1569, 1581, 1629, 1641, 1929, 1941, 1989, 2001, 2049, 2061, 2559, 2571, 2619, 2631, 2679, 2691, 2979, 2991, 3039

Offset: 1

Author

Amiram Eldar, May 23 2023

Keywords

• nonn
• base

Comments

All the terms above 1 are odd multiples of 3.

The partial sums of the primorials (A143293) are terms, since the primorial-base representation of A143293(n) is n+1 1's.

Examples

			3 is a term since its primorial-base presentation, 11, has only odd digits.
21 is a term since its primorial-base presentation, 311, has only odd digits.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..14620 (terms below A002110(8) = 19#)
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A002110, A049345, A328849.

Subsequence: A143293.

Similar sequences: A003462 \ {0} (ternary), A014261 (decimal), A032911 (base 4), A032912 (base 5), A033032 (base 6), A033033 (base 7), A033034 (base 8), A033035 (base 9), A033036 (base 11), A033037 (base 12), A033038 (base 13), A033039 (base 14), A033040 (base 15), A033041 (base 16), A126646 (binary), A351894 (factorial base).

Programs

Mathematica

With[{max = 5}, bases = Prime@ Range[max, 1, -1]; nmax = Times @@ bases - 1; prmBaseDigits[n_] := IntegerDigits[n, MixedRadix[bases]]; Select[Range[1, nmax, 2], AllTrue[prmBaseDigits[#], OddQ] &]]

PARI

is(n) = {my(p = 2); if(n < 1, return(0)); while(n > 0, if((n%p)%2 == 0, return(0)); n \= p; p = nextprime(p+1)); return(1);}