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 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 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 A266478 A107389 Adjacent sequences: A363240 A363241 A363242 * A363244 A363245 A363246 KEYWORD nonn,base AUTHOR Amiram Eldar, May 23 2023 STATUS approved

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