A363244 Numbers that in primorial-base representation have digits with an alternating parity.

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, ...).

Links

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

Index entries for sequences related to primorial base.

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

Cf. A002110, A049345.

Similar sequences: A000975 (binary), A030141 (decimal), A033068 (ternary), A179970 (quaternary), A351897 (factorial base).

Sequence in context: A327952 A099835 A133436 * A351897 A184676 A191175

Adjacent sequences: A363241 A363242 A363243 * A363245 A363246 A363247

Keyword

nonn,base

Author

Amiram Eldar, May 23 2023

Status

approved