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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A333314 A238575 A020144 * A075933 A075929 A334530

Adjacent sequences:  A235037 A235038 A235039 * A235041 A235042 A235043

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 02 2014

STATUS

approved

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Last modified August 7 11:08 EDT 2020. Contains 336275 sequences. (Running on oeis4.)