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

1,2

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.

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.

Example

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.

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] &]]

Prog

(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); }

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).

Sequence in context: A048780 A009864 A128127 * A341433 A014857 A177817

Adjacent sequences: A363239 A363240 A363241 * A363243 A363244 A363245

Keyword

nonn,base

Author

Amiram Eldar, May 23 2023

Status

approved