login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A363243 Numbers with an equal number of odd and even digits in their primorial-base 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 (list; graph; refs; listen; history; text; internal format)
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
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
Similar sequences: A031443 (binary), A227870 (decimal), A351895 (factorial base).
Sequence in context: A219273 A000133 A059086 * A215168 A266478 A107389
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, May 23 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 1 19:16 EST 2024. Contains 370443 sequences. (Running on oeis4.)