cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A361997 Records in A361902.

Original entry on oeis.org

3, 4, 5, 9, 12, 15, 24, 1470, 3873, 25224
Offset: 1

Views

Author

Pontus von Brömssen, Apr 02 2023

Keywords

Comments

Either a(11) = 27474 = A361902(27727) or a(11) = A361902(k) > 60000, where k is one of 7123, 11009, and 23843.

Crossrefs

Cf. A263875, A361902, A361998.

A361998 Indices of records in A361902.

Original entry on oeis.org

0, 8, 24, 25, 85, 91, 121, 153, 175, 6313
Offset: 1

Views

Author

Pontus von Brömssen, Apr 02 2023

Keywords

Comments

a(11) is one of 7123, 11009, 23843, and 27727.

Crossrefs

Cf. A263874, A361902, A361997.

A361999 a(n) is the smallest k such that A361902(k) = n, or -1 if no such k exists.

Original entry on oeis.org

2, 1, -1, 0, 8, 24, 33, 90, 116, 25, 402, 140, 85, 120, 692, 91, 472, 1240, 369, 762, 694, 551, 3290, 322, 121, 2758, 1164, 321, 778, 3144, 663, 3418, 4684, 721, 8590, 3222, 511, 7424, 5202, 391, 3364, 10392, 531, 9710, 1714, 891, 27116, 11008, 703, 19132, 8898
Offset: 0

Views

Author

Pontus von Brömssen, Apr 02 2023

Keywords

Links

Crossrefs

Cf. A260350, A361902.

A363533 Least k such that n*F(k)+1 is prime, where F = A000045 is the Fibonacci sequence, or -1 if no such k exists.

Original entry on oeis.org

1, 1, 3, 1, 3, 1, 9, 3, 3, 1, 3, 1, 9, 3, 3, 1, 6, 1, 9, 3, 3, 1, 3, 4, 18, 3, 9, 1, 3, 1, 15, 4, 3, 4, 3, 1, 9, 5, 3, 1, 3, 1, 48, 3, 9, 1, 24, 3, 9, 3, 3, 1, 3, 3, 9, 3, 6, 1, 24, 1, 36, 5, 3, 4, 3, 1, 12, 3, 3, 1, 6, 1, 12, 3, 3, 4, 6, 1, 9, 4, 3, 1, 3, 5
Offset: 1

Views

Author

Pontus von Brömssen, Jun 09 2023

Keywords

Comments

2 does not appear because F(1) = F(2).
a(n) is divisible by 3 if n >= 3 is odd (unless a(n) = -1), because F(k) is odd (so n*F(k)+1 > 2 is even) when k is not divisible by 3.

Examples

			For n = 17, the least k such that 17*F(k)+1 is prime is k = 6, with 17*F(6)+1 = 17*8+1 = 137, so a(17) = 6.

Crossrefs

Cf. A000045, A034693, A124067, A361902, A362376, A363534 (records), A363535 (indices of records), A363536 (first occurrences).

Programs

  • Mathematica
    Array[(k = 1; While[! PrimeQ[# Fibonacci[k] + 1], k++]; k) &, 85] (* Michael De Vlieger, Jun 10 2023 *)
  • PARI
    a(n) = my(k=1); while(!isprime(n*fibonacci(k)+1), k++); k; \\ Michel Marcus, Jun 10 2023
  • Python
    from sympy import isprime, fibonacci
from itertools import count
def A363533(n):
    # Note: the function hangs if a(n) = -1.
    return next(k for k in count(1) if isprime(n*fibonacci(k)+1))

Formula

a(n) = 1 if and only if n+1 is prime.

A361509 a(n) = smallest Fibonacci number F(k) such that F(k) + F(n) is a prime, or -1 if no such F(k) exists.

Original entry on oeis.org

2, 1, 1, 0, 0, 0, 3, 0, 2, 3, 34, 0, 5, 0, 2, 3, 34, 0, 987, 46368, 2584, 3, 2, 0, 13, 144
Offset: 0

Views

Author

Jack Braxton, Mar 26 2023

Keywords

Comments

a(26) is currently unknown.
a(26) > 10^7000 if it is not -1. - Robert Israel, Apr 03 2023

Crossrefs

Cf. A000045, A361510, A361902.

Programs

  • Maple
    with(combinat):
a:=[]; b:=[]; for n from 0 to 25 do
k:=0; t1:=fibonacci(n);
while not isprime( fibonacci(k)+t1) do k:=k+1; od:
a:=[op(a),fibonacci(k)]; b:=[op(b),k];
od:
a; # A361509
b; # A361510
  • Mathematica
    a[n_] := Module[{fn = Fibonacci[n], k = 0}, While[! PrimeQ[fn + Fibonacci[k]], k++]; Fibonacci[k]]; Array[a, 26, 0] (* Amiram Eldar, Mar 30 2023 *)
  • PARI
    a(n) = my(k=0, fn=fibonacci(n)); while (!isprime(fn+fibonacci(k)), k++); fibonacci(k); \\ Michel Marcus, Mar 30 2023

Formula

a(n) = A000045(A361902(A000045(n))) (unless A361902(A000045(n)) = -1). - Pontus von Brömssen, Mar 30 2023

Extensions

Edited by N. J. A. Sloane, Mar 30 2023

A361510 a(n) = smallest k >= 0 such that Fibonacci(k) + Fibonacci(n) is a prime, or -1 if no such k exists.

Original entry on oeis.org

3, 1, 1, 0, 0, 0, 4, 0, 3, 4, 9, 0, 5, 0, 3, 4, 9, 0, 16, 24, 18, 4, 3, 0, 7, 12
Offset: 0

Views

Author

Jack Braxton, Mar 26 2023

Keywords

Comments

a(26) is currently unknown.

Crossrefs

Cf. A000045, A361509, A361902.

Programs

  • Maple
    See A361509.
  • Mathematica
    a[n_] := Module[{fn = Fibonacci[n], k = 0}, While[! PrimeQ[fn + Fibonacci[k]], k++]; k]; Array[a, 26, 0] (* Amiram Eldar, Mar 30 2023 *)
  • PARI
    a(n) = my(k=0, fn=fibonacci(n)); while (!isprime(fn+fibonacci(k)), k++); k; \\ Michel Marcus, Mar 30 2023

Formula

a(n) = A361902(A000045(n)). - Pontus von Brömssen, Mar 30 2023

Extensions

Edited by N. J. A. Sloane, Mar 30 2023
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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