A363533 -id:A363533 - cp's OEIS frontend

A363534 Records in A363533.

1, 3, 9, 18, 48, 60, 540, 1998, 2844, 3045, 39753

Offset: 1

Pontus von Brömssen, Jun 09 2023

Cf. A361997, A363533, A363535.

Union@ FoldList[Max, Array[(k = 1; While[! PrimeQ[# Fibonacci[k] + 1], k++]; k) &, 3000]] (* Michael De Vlieger, Jun 10 2023 *)

A363535 Indices of records in A363533.

Original entry on oeis.org

1, 3, 7, 25, 43, 139, 227, 263, 727, 2463, 3541

Offset: 1

Pontus von Brömssen, Jun 09 2023

a(12) = 9043 unless A363533(9043) = -1.

Cf. A361998, A363533, A363534.

s = Array[(k = 1; While[! PrimeQ[# Fibonacci[k] + 1], k++]; k) &, 3000]; t = Union@ FoldList[Max, s]; Array[FirstPosition[s, t[[#]]][[1]] &, Length[t]] (* Michael De Vlieger, Jun 10 2023 *)

A363536 a(n) is the smallest k such that A363533(k) = n, or -1 if no such k exists.

Original entry on oeis.org

1, -1, 3, 24, 38, 17, 142, 248, 7, 328, 528, 67, 446, 1676, 31, 208, 1828, 25, 656, 788, 203, 4700, 1678, 47, 5368, 1270, 87, 2992, 10712, 317, 12034, 9262, 121, 5248, 11744, 61, 2798, 19598, 481, 3628, 8956, 181, 4388, 18694, 383, 22754, 23836, 43, 8212, 34636

Offset: 1

Pontus von Brömssen, Jun 09 2023

sign

Cf. A361999, A363533.

A362376 a(n) is the least k such that Fibonacci(n)*Fibonacci(k) + 1 is a prime, and -1 if no such k exists.

Original entry on oeis.org

1, 1, 1, 3, 3, 3, 9, 3, 4, 9, 3, 4, 3, 27, 4, 24, 24, 4, 3, 6, 3, 3, 444, 3, 12, 9, 3, 63, 6, 8, 36, 6, 36, 12, 12, 4, 21, 60, 4, 3, 24, 73, 51, 3, 11, 51, 12, 4, 504, 12, 3, 33, 21, 6, 9, 6, 4, 384, 21, 7, 54, 3, 4, 51, 24, 63, 30, 24, 11, 45, 72, 6, 39, 9, 22, 42, 12, 16, 60, 30

Offset: 1

Jack Braxton, Apr 17 2023

nonn

The frequencies seem interesting. In the early terms, 5 appears notably rarely, i.e., not until at a(240), whereas several other numbers appear notably frequently, e.g., 24 appears 13 times before a(240). - Peter Munn, May 03 2023

			For n=4, Fibonacci(4)=3 and 3*Fibonacci(k)+1 is not prime until k reaches 3, so a(4)=3.

Chai Wah Wu, Table of n, a(n) for n = 1..448

Cf. A000040, A000045, A034693, A363533.

Table[m = Fibonacci[n]; k = 1; While[! PrimeQ[m*Fibonacci[k] + 1], k++]; k, {n, 120}] (* Michael De Vlieger, May 03 2023 *)

a(n) = my(F=fibonacci(n), k=1); while (!ispseudoprime(F*fibonacci(k) + 1), k++); k; \\ Michel Marcus, Apr 18 2023

from itertools import count
from sympy import fibonacci, isprime
def A362376(n):
    a = b = fibonacci(n)
    for k in count(1):
        if isprime(a+1):
            return k
        a, b = b, a+b # Chai Wah Wu, May 03 2023

a(n) = A363533(A000045(n)). - Pontus von Brömssen, Jun 20 2023

More terms from Michel Marcus, Apr 18 2023

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A363534 Records in A363533.

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A363535 Indices of records in A363533.

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A363536 a(n) is the smallest k such that A363533(k) = n, or -1 if no such k exists.

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A362376 a(n) is the least k such that Fibonacci(n)*Fibonacci(k) + 1 is a prime, and -1 if no such k exists.

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