A049997 -id:A049997 - cp's OEIS frontend

A254122 Numbers requiring two Fibonacci numbers to build using + or *.

4, 6, 7, 9, 10, 11, 14, 15, 16, 18, 22, 23, 24, 25, 26, 29, 35, 36, 37, 39, 40, 42, 47, 56, 57, 58, 60, 63, 64, 65, 68, 76, 90, 91, 92, 94, 97, 102, 104, 105, 110, 123, 145, 146, 147, 149, 152, 157, 165, 168, 169, 170, 178, 199

Offset: 1

R. J. Mathar, Jan 25 2015

nonn

Numbers of the form F(i)+F(k) or F(i)*F(k), F=A000045, but not in A000045 themselves.

Supersequence of A179242; contains also numbers like 5*5=25, 5*8=40, 8*8=64 and 5*13=65. (Note that we count 8 twice in 8*8=64, including its multiplicity.)

Cf. A025282, A049997.

A272916 Numbers that are a product of two Fibonacci (A000045) numbers or a product of two Lucas (A000032) numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 21, 24, 25, 26, 28, 29, 33, 34, 39, 40, 42, 44, 47, 49, 54, 55, 63, 64, 65, 68, 72, 76, 77, 87, 89, 102, 104, 105, 110, 116, 121, 123, 126, 141, 144, 165, 168, 169, 170, 178, 188, 198, 199, 203, 228, 233

Offset: 1

Clark Kimberling, May 10 2016

Conjecture: if c and d are consecutive terms, then d - c is a term.

			Equals union(A049997, A272909), in increasing order.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A000032, A000045, A049997, A272909, A272917 (difference sequence).

z = 400; u2 = Sort[Flatten[Table[Fibonacci[i + 1] * Fibonacci[j + 1], {i, 1, z}, {j, i, z}]]];
v2 = Sort[Flatten[Table[LucasL[i]*LucasL[j], {i, 1, z}, {j, i, z}]]];
u = Take[Union[u2, v2], 200] (* A272916 *)
d = Take[Differences[u], 200]  (* A272917 *)

A276281 Numbers of the form Bell(i)*Bell(j).

Original entry on oeis.org

1, 2, 4, 5, 10, 15, 25, 30, 52, 75, 104, 203, 225, 260, 406, 780, 877, 1015, 1754, 2704, 3045, 4140, 4385, 8280, 10556, 13155, 20700, 21147, 41209, 42294, 45604, 62100, 105735, 115975, 178031, 215280, 231950, 317205, 579875, 678570, 769129, 840420, 1099644

Offset: 1

Vincenzo Librandi, Sep 04 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A000110, A049997, A272909.

Take[Union@Flatten@Table[BellB[i] BellB[j], {i, 0, 60}, {j, i}], 60]

use ntheory ":all"; my($l,$i,%BP)=(50,0); my @Bell = map { my $n=$; vecsum(map { stirling($n,$,2) } 0..$n); } 0..$l;  for my $i (0..$l) { for my $j ($i..$l) { $BP{vecprod($Bell[$i],$Bell[$j])}++ } }  say $i++," $" for sort {$a<=>$b} keys %BP;  # _Dana Jacobsen, Sep 07 2016

A131511 All possible products of prime and Fibonacci numbers.

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 79, 82, 83, 85, 86, 87, 88, 89, 91, 93, 94, 95, 97, 101, 102, 103, 104, 105

Offset: 1

Tanya Khovanova, Aug 14 2007

nonn

This sequence contains all prime numbers as a subsequence because 1 is a Fibonacci number. Similarly it contains all even semiprimes.

			8 is not in this sequence because the only way to represent 8 as a product of a prime and some number is 2*4 and 4 is not a Fibonacci number.
105 is in this sequence because 105 = 3*21 and 3 is a prime number and 21 is a Fibonacci number.

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A000045, A001358, A049997, A132147.

Take[Union[Flatten[Table[Fibonacci[n]*Prime[k], {n, 70}, {k, 70}]]], 70]

isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
isok(n) = {if (n==0, return (1)); my(f=factor(n)); for (k=1, #f~, p = f[k, 1]; if (isfib(n/p), return (1)););} \\ Michel Marcus, Apr 19 2018

A228523 Numbers that are not the product of two Fibonacci numbers (not necessarily distinct).

Original entry on oeis.org

7, 11, 12, 14, 17, 18, 19, 20, 22, 23, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92

Offset: 1

Alonso del Arte, Sep 02 2013

All primes except prime Fibonacci numbers are in this sequence.

			Although 12 can be expressed as a product of Fibonacci numbers, it takes three of them, not two, hence 12 is in the list.
There is no way to express 14 as a product of Fibonacci numbers since its larger prime factor, 7, is not a Fibonacci number, hence 14 is in the list.
16 is not in the list because it can be expressed as 2 * 8.

Cf. A049997 (complement).

nn = 12; f = Fibonacci[Range[2, nn]]; f2 = Select[Union[Flatten[Outer[Times, f, f]]], # <= f[[-1]] &]; Complement[Range[f[[-1]]], f2] (* T. D. Noe, Sep 03 2013 *)

A276828 Numbers of the form Bell(i)*Fibonacci(j).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 10, 13, 15, 16, 21, 25, 26, 30, 34, 40, 42, 45, 52, 55, 65, 68, 75, 89, 104, 105, 110, 120, 144, 156, 170, 178, 195, 203, 233, 260, 275, 288, 315, 377, 406, 416, 445, 466, 510, 609, 610, 676, 720, 754, 825, 877, 987, 1015, 1092, 1165

Offset: 1

Vincenzo Librandi, Sep 20 2016

nonn

Cf. A000110, A049997, A272909, A276281.

lim=10^6; Union@ Reap[ Sow[0]; For[i = 2, (f = Fibonacci[i]) < lim, i++, For[ j=1, (p = BellB[j] f) < lim, j++, Sow@ p]]][[2, 1]] (* Giovanni Resta, Oct 03 2016 *)

cp's OEIS Frontend

A254122 Numbers requiring two Fibonacci numbers to build using + or *.

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A272916 Numbers that are a product of two Fibonacci (A000045) numbers or a product of two Lucas (A000032) numbers.

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A276281 Numbers of the form Bell(i)*Bell(j).

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Perl

A131511 All possible products of prime and Fibonacci numbers.

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PARI

A228523 Numbers that are not the product of two Fibonacci numbers (not necessarily distinct).

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Mathematica

A276828 Numbers of the form Bell(i)*Fibonacci(j).

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Mathematica