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URL: https://oeis.org/A363244

⇱ A363244 - OEIS

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A363244
Numbers that in primorial-base representation have digits with an alternating parity.
1
0, 1, 2, 5, 7, 11, 14, 19, 23, 26, 32, 44, 56, 67, 71, 79, 83, 92, 104, 116, 127, 131, 139, 143, 152, 164, 176, 187, 191, 199, 203, 217, 221, 229, 233, 277, 281, 289, 293, 337, 341, 349, 353, 397, 401, 409, 413, 452, 464, 476, 512, 524, 536, 572, 584, 596, 637
OFFSET
1,3
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, ...).
EXAMPLE
7 is a term since its primorial-base representation is 101 and the parities of its digits are odd, even, odd.
MATHEMATICA
With[{max = 5}, bases = Prime@ Range[max, 1, -1]; nmax = Times @@ bases - 1; q[n_] := AllTrue[Differences@ Mod[IntegerDigits[n, MixedRadix[bases]], 2], # != 0 &]; Select[Range[0, nmax], q]]
PROG
(PARI) is(n) = {my(p = 3, r1 = n%2); n \= 2; while(n > 0, r2 = (n%p)%2; n \= p; p = nextprime(p+1); if(r1 == r2, return(0)); r1 = r2); 1; }
CROSSREFS
Similar sequences: A000975 (binary), A030141 (decimal), A033068 (ternary), A179970 (quaternary), A351897 (factorial base).
Sequence in context: A327952 A099835 A133436 * A351897 A184676 A191175
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, May 23 2023
STATUS
approved