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A363242
Numbers whose primorial-base representation contains only odd digits.
1
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.
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
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, May 23 2023
STATUS
approved