

A363243


Numbers with an equal number of odd and even digits in their primorialbase representation.


1



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
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OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

5 is a term since its primorialbase 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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



