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%I #29 Feb 05 2014 10:55:14
%S 0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,22,23,24,26,28,29,30,
%T 31,32,34,37,38,40,41,43,44,46,47,48,51,52,53,56,58,59,60,61,62,64,67,
%U 68,71,73,74,76,79,80,82,83,85,86,88,89,92,94,95,96,97,101
%N Numbers whose prime divisors, when multiplied together without carry-bits (as encodings of GF(2)[X]-polynomials, with A048720), produce the original number; numbers for which A234741(n) = n.
%C If n is present, then 2n is present also, as shifting binary representation left never produces any carries.
%H Antti Karttunen, <a href="/A235034/b235034.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on (or containing) GF(2)[X]-polynomials</a>
%e All primes occur in this sequence as no multiplication -> no need to add any intermediate products -> no carry bits produced.
%e Composite numbers like 15 are also present, as 15 = 3*5, and when these factors (with binary representations '11' and '101') are multiplied as:
%e 101
%e 1010
%e ----
%e 1111 = 15
%e we see that the intermediate products 1*5 and 2*5 can be added together without producing any carry-bits (as they have no 1-bits in the same columns/bit-positions), so A048720(3,5) = 3*5 and thus 15 is included in this sequence.
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A235034 (MATCHING-POS 1 0 (lambda (n) (or (zero? n) (= n (reduce A048720bi 1 (ifactor n)))))))
%Y Gives the positions of zeros in A236378, i.e., n such that A234741(n) = n.
%Y Intersection with A235035 gives A235032.
%Y Other subsequences: A000040 (A091206 and also A091209), A045544 (A004729), A093641, A235040 (gives odd composites in this sequence), A235050, A235490.
%Y Cf. A048720, A061858, A234741.
%K nonn
%O 1,3
%A _Antti Karttunen_, Jan 02 2014
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