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%I #10 May 25 2023 07:27:36
%S 1,3,9,21,39,51,99,111,159,171,249,261,309,321,369,381,669,681,729,
%T 741,789,801,1089,1101,1149,1161,1209,1221,1509,1521,1569,1581,1629,
%U 1641,1929,1941,1989,2001,2049,2061,2559,2571,2619,2631,2679,2691,2979,2991,3039
%N Numbers whose primorial-base representation contains only odd digits.
%C All the terms above 1 are odd multiples of 3.
%C The partial sums of the primorials (A143293) are terms, since the primorial-base representation of A143293(n) is n+1 1's.
%H Amiram Eldar, <a href="/A363242/b363242.txt">Table of n, a(n) for n = 1..14620</a> (terms below A002110(8) = 19#)
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%e 3 is a term since its primorial-base presentation, 11, has only odd digits.
%e 21 is a term since its primorial-base presentation, 311, has only odd digits.
%t 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] &]]
%o (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);}
%Y Cf. A002110, A049345, A328849.
%Y Subsequence: A143293.
%Y 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).
%K nonn,base
%O 1,2
%A _Amiram Eldar_, May 23 2023