A351897 -id:A351897 - cp's OEIS frontend

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

Amiram Eldar, May 23 2023

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, ...).

			7 is a term since its primorial-base representation is 101 and the parities of its digits are odd, even, odd.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Index entries for sequences related to primorial base.

Cf. A002110, A049345.

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

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]]

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; }

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI