A135952 -id:A135952 - cp's OEIS frontend

A240238 a(n) is the prime p for which A135952(n) divides Fibonacci(p).

19, 37, 19, 37, 79, 97, 67, 139, 157, 59, 97, 199, 229, 31, 307, 337, 113, 367, 379, 439, 53, 163, 499, 89, 547, 577, 607, 619, 727, 829, 877, 937, 313, 967, 487, 997, 1009, 1069, 37, 373, 577, 389, 31, 1237, 1279, 1297, 229, 463, 41, 1399, 1429, 727, 1459, 1609, 1627, 1657, 1759, 593, 1867, 223, 2029, 2089, 2137, 1087, 2179, 61, 773, 263, 409, 2467

Offset: 1

Hans Havermann, Apr 02 2014

nonn

			a(1) is 19 because A135952(1) = 37 divides Fibonacci(19).
a(2) is 37 because A135952(2) = 73 divides Fibonacci(37).
a(3) is 19 because A135952(3) = 113 divides Fibonacci(19).
a(4) is 37 because A135952(4) = 149 divides Fibonacci(37).

Hans Havermann, Table of n, a(n) for n = 1..5000

Cf. A135952, A240239.

A240239 a(n) is one-half of the integer approximated by A135952(n)/A240238(n).

Original entry on oeis.org

1, 1, 3, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 9, 1, 1, 3, 1, 1, 1, 9, 3, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 30, 3, 2, 3, 39, 1, 1, 1, 6, 3, 34, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 9, 1, 1, 1, 2, 1, 37, 3, 9, 6, 1, 8, 1, 1, 2, 1, 3, 2, 10, 1, 1, 11, 19, 3, 1, 1, 1, 1, 2, 1, 1, 7, 1, 47, 3, 3, 1, 1, 2, 1, 1

Offset: 1

Hans Havermann, Apr 02 2014

nonn

The integer approximation can be made exact by first adding 1 to A135952(n) where a(n) is odd, or subtracting 1 from A135952(n) where a(n) is even, before dividing by A240238(n).

Conjecture: a(n) never ends with the digit 5.

			(A135952(1)+1)/A240238(1) = (37+1)/19 = 2, so a(1) is 2/2 = 1.
(A135952(2)+1)/A240238(2) = (73+1)/37 = 2, so a(2) is 2/2 = 1.
(A135952(3)+1)/A240238(3) = (113+1)/19 = 6, so a(3) is 6/2 = 3.
(A135952(4)-1)/A240238(4) = (149-1)/37 = 4, so a(4) is 4/2 = 2.

Hans Havermann, Table of n, a(n) for n = 1..5000
Hans Havermann, Magic multipliers

Cf. A135952, A240238.

A038672 Primes p such that the p-th Fibonacci number is composite.

Original entry on oeis.org

19, 31, 37, 41, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 109, 113, 127, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337

Offset: 1

Jeff Burch

nonn

Hans Havermann, Table of n, a(n) for n = 1..10000
Hans Havermann, Composite Prime-Index Fibonacci Numbers Factored

Cf. A090819 (essentially identical), A083668, A135952.

Rest[Select[Prime[Range[68]], ! PrimeQ[Fibonacci[#]] &]] (* Jayanta Basu, Jul 10 2013 *)
s={A083668}; Complement[Prime[Range[2, 10034]], s] (* Hans Havermann, Feb 12 2014 *)

A238082 Composites occurring as divisors of Fibonacci(p) with p prime.

Original entry on oeis.org

4181, 10877, 75077, 162133, 330929, 1256293, 1346269, 2662277, 3636121, 4226777, 9401893, 13455077, 14787181, 16485493, 21692189, 24157817, 24493061, 25532501, 29604893, 31432381, 39247393, 73780877, 75245777, 77337941, 120485381, 124477513, 127835341, 132162581, 143221993, 143548501

Offset: 1

Hans Havermann, Antti Karttunen and David W. Wilson, Feb 02 2014

nonn

The first two non-semiprimes are a(16) = 73 * 149 * 2221 and a(254) = 1453 * 2909 * 10177.

David Wilson and Hans Havermann, Table of n, a(n) for n = 1..338 [David Wilson to 148, Hans Havermann to 338]
Hans Havermann, A238082 factored
Hans Havermann, Composite Prime-Index Fibonacci Numbers Factored
Antti Karttunen, More composite terms for A233281

The sequence gives composite values of A233281.

Cf. A038672, A092395, A135952.

cp's OEIS Frontend

A240238 a(n) is the prime p for which A135952(n) divides Fibonacci(p).

Views

Author

Keywords

Examples

Links

Crossrefs

A240239 a(n) is one-half of the integer approximated by A135952(n)/A240238(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A038672 Primes p such that the p-th Fibonacci number is composite.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A238082 Composites occurring as divisors of Fibonacci(p) with p prime.

Views

Author

Keywords

Comments

Links

Crossrefs