A235040 After 1, composite odd numbers, whose prime divisors, when multiplied together without carry-bits (as codes for GF(2)[X]-polynomials, with A048720), yield the same number back.

1, 15, 51, 85, 95, 111, 119, 123, 187, 219, 221, 255, 335, 365, 411, 447, 485, 511, 629, 655, 685, 697, 771, 831, 879, 959, 965, 1011, 1139, 1241, 1285, 1405, 1535, 1563, 1649, 1731, 1779, 1799, 1923, 1983, 2005, 2019, 2031, 2045, 2227, 2605, 2735, 2815, 2827

Offset

0,2

Comments

Note: Start indexing from n=1 if you want just composite numbers. a(0)=1 is the only nonprime, noncomposite in this list.

The first term with three prime divisors is a(11) = 255 = 3*5*17.

The next terms with three prime divisors are

255, 3855, 13107, 21845, 24415, 28527, 30583, 31215, 31611, 31695, 32691, 48059, 56283, 56797, 61935, 65365, 87805, 98005, ...

Of these 24415 (= 5*19*257) is the first one with at least one prime factor that is not a Fermat prime (A019434).

The first term with four prime divisors is a(427) = 65535 = 3*5*17*257.

The first terms which are not multiples of any Fermat prime are: 511, 959, 3647, 4039, 4847, 5371, 7141, 7231, 7679, 7913, 8071, 9179, 12179, ... (511 = 7*73, 959 = 7*137, ...)

Links

Antti Karttunen, Table of n, a(n) for n = 0..511

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

Example

15 = 3*5. 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 A235040 (MATCHING-POS 0 1 (lambda (n) (and (odd? n) (not (prime? n)) (= n (reduce A048720bi 1 (ifactor n)))))))

Crossrefs

Odd nonprimes in A235034. A235039 is a subsequence.

The composite terms in A045544 (A004729) all occur also here.

Cf. also A019434, A048720, A235045, A235050, A115857, A115872.

Sequence in context: A238575 A020144 A339880 * A365473 A075933 A075929

Adjacent sequences: A235037 A235038 A235039 * A235041 A235042 A235043

Keyword

nonn

Author

Antti Karttunen, Jan 02 2014

Status

approved