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%I #8 May 25 2023 07:27:59
%S 0,1,2,5,7,11,14,19,23,26,32,44,56,67,71,79,83,92,104,116,127,131,139,
%T 143,152,164,176,187,191,199,203,217,221,229,233,277,281,289,293,337,
%U 341,349,353,397,401,409,413,452,464,476,512,524,536,572,584,596,637
%N Numbers that in primorial-base representation have digits with an alternating parity.
%C 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, ...).
%H Amiram Eldar, <a href="/A363244/b363244.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%e 7 is a term since its primorial-base representation is 101 and the parities of its digits are odd, even, odd.
%t 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]]
%o (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; }
%Y Cf. A002110, A049345.
%Y Similar sequences: A000975 (binary), A030141 (decimal), A033068 (ternary), A179970 (quaternary), A351897 (factorial base).
%K nonn,base
%O 1,3
%A _Amiram Eldar_, May 23 2023
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