A235034 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.

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, 31, 32, 34, 37, 38, 40, 41, 43, 44, 46, 47, 48, 51, 52, 53, 56, 58, 59, 60, 61, 62, 64, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 85, 86, 88, 89, 92, 94, 95, 96, 97, 101

Offset

1,3

Comments

If n is present, then 2n is present also, as shifting binary representation left never produces any carries.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences operating on (or containing) GF(2)[X]-polynomials

Example

All primes occur in this sequence as no multiplication -> no need to add any intermediate products -> no carry bits produced.
Composite numbers like 15 are also present, as 15 = 3*5, and when these factors (with binary representations '11' and '101') are multiplied as:
   101
  1010
  ----
  1111 = 15
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.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A235034 (MATCHING-POS 1 0 (lambda (n) (or (zero? n) (= n (reduce A048720bi 1 (ifactor n)))))))

Crossrefs

Gives the positions of zeros in A236378, i.e., n such that A234741(n) = n.

Intersection with A235035 gives A235032.

Other subsequences: A000040 (A091206 and also A091209), A045544 (A004729), A093641, A235040 (gives odd composites in this sequence), A235050, A235490.

Cf. A048720, A061858, A234741.

Sequence in context: A306202 A328335 A302569 * A331682 A107037 A031994

Adjacent sequences: A235031 A235032 A235033 * A235035 A235036 A235037

Keyword

nonn

Author

Antti Karttunen, Jan 02 2014

Status

approved