cp's OEIS Frontend

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

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