A363243 Numbers with an equal number of odd and even digits in their primorial-base representation.

2, 5, 31, 32, 35, 36, 40, 43, 44, 47, 48, 52, 55, 56, 59, 63, 67, 68, 71, 75, 79, 80, 83, 87, 91, 92, 95, 96, 100, 103, 104, 107, 108, 112, 115, 116, 119, 123, 127, 128, 131, 135, 139, 140, 143, 147, 151, 152, 155, 156, 160, 163, 164, 167, 168, 172, 175, 176, 179

Offset

1,1

Comments

The sum of the first k odd-indexed primorial numbers (A002110) is a term, since its primorial-base representation is 1010...10, with the block "10" repeated k times (these numbers are 2, 32, 2342, 512852, 223605722, ...).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base.

Example

5 is a term since its primorial-base representation, 21, has one odd digit, 1, and one even digit, 2.

Mathematica

With[{max = 5}, bases = Prime@ Range[max, 1, -1]; nmax = Times @@ bases - 1; prmBaseDigits[n_] := IntegerDigits[n, MixedRadix[bases]]; Select[Range[nmax], EvenQ[Length[(d = prmBaseDigits[#])]] && Count[d, _?EvenQ] == Length[d]/2 &]]

Prog

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

Crossrefs

Cf. A002110, A049345.

Similar sequences: A031443 (binary), A227870 (decimal), A351895 (factorial base).

Sequence in context: A219273 A000133 A059086 * A215168 A370830 A266478

Adjacent sequences: A363240 A363241 A363242 * A363244 A363245 A363246

Keyword

nonn,base

Author

Amiram Eldar, May 23 2023

Status

approved