A138185 -id:A138185 - cp's OEIS frontend

A138184 Largest prime not exceeding Fibonacci(n) = A000045(n).

2, 3, 5, 7, 13, 19, 31, 53, 89, 139, 233, 373, 607, 983, 1597, 2579, 4177, 6763, 10939, 17707, 28657, 46351, 75017, 121379, 196387, 317797, 514229, 832003, 1346249, 2178283, 3524569, 5702867, 9227443, 14930341, 24157811, 39088157, 63245971

Offset: 3

Colm Mulcahy, Mar 04 2008

			a(8) = 19 because 19 is the largest prime not exceeding 21 = A000045(8).

Harry J. Smith, Table of n, a(n) for n = 3..657

Cf. A138181, A138182, A138183, A138185.

A138184 := proc(n) prevprime(combinat[fibonacci](n)+1) ; end: seq(A138184(n),n=3..45) ; # R. J. Mathar, Apr 22 2008

PrimePrev[n_]:=Module[{k=n},While[ !PrimeQ[k],k-- ];k];f[n_]:=Fibonacci[n];lst={};Do[AppendTo[lst,PrimePrev[f[n]]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2010 *)

a(n) = A000040(A054782(n)). - R. J. Mathar, Apr 22 2008

Edited and extended by R. J. Mathar, Apr 22 2008

Offset changed from 4 to 3 by Harry J. Smith, Jan 02 2009

A138183 Smallest Fibonacci number not less than the n-th prime.

Original entry on oeis.org

2, 3, 5, 8, 13, 13, 21, 21, 34, 34, 34, 55, 55, 55, 55, 55, 89, 89, 89, 89, 89, 89, 89, 89, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 377, 377

Offset: 1

Colm Mulcahy, Mar 04 2008

			a(4) = 8 because the 8 is the smallest Fibonacci number not less than 7 (the 4th prime).

Cf. A138182, A138185.

With[{fibs=Fibonacci[Range[20]]},Table[SelectFirst[fibs,#>=n&],{n,Prime[ Range[60]]}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 22 2018 *)

a(n) = {p = prime(n); i = 0; until ((f = fibonacci(i)) >= p, i++); f;} \\ Michel Marcus, Aug 31 2013

A375751 a(n) is the difference between F=A000045(n) and the largest prime not exceeding F.

Original entry on oeis.org

0, 0, 0, 1, 0, 2, 3, 2, 0, 5, 0, 4, 3, 4, 0, 5, 4, 2, 7, 4, 0, 17, 8, 14, 31, 14, 0, 37, 20, 26, 9, 20, 22, 11, 6, 12, 15, 32, 18, 17, 0, 16, 43, 24, 0, 17, 20, 26, 27, 20, 6, 9, 12, 34, 29, 36, 30, 47, 48, 4, 45, 32, 54, 27, 132, 22, 31, 4, 32, 11, 12, 60, 7, 76

Offset: 3

Hugo Pfoertner, Aug 27 2024

Amiram Eldar, Table of n, a(n) for n = 3..10000

Cf. A000045, A007917, A001605, A138184, A138185, A159977, A159978, A202090.

a:= n-> (F-> F-prevprime(F+1))(combinat[fibonacci](n)):
seq(a(n), n=3..76);  # Alois P. Heinz, Aug 27 2024

a[n_]:=Module[{p=2},While[(f=Fibonacci[n])>=p, pold=p;p=NextPrime[p]]; d=f-pold;If[d>0,f-pold,d=0]; d]; Array[a,74,3] (* Stefano Spezia, Aug 27 2024 *)
Map[(# - NextPrime[# + 1, -1]) &, Fibonacci[Range[3, 76]]] (* Amiram Eldar, Aug 29 2024 *)

a(n) = my(F=fibonacci(n)); F-precprime(F)

from sympy import prevprime, fibonacci
def A375753(n): return (F:=fibonacci(n)) - prevprime(F+1) # Karl-Heinz Hofmann, Aug 27 2024

a(n) = A000045(n) - A138184(n).

a(n) = 0 <=> n in { A001605 }. - Alois P. Heinz, Aug 27 2024

A218557 Smallest prime >= n-th Lucas number.

Original entry on oeis.org

2, 2, 3, 5, 7, 11, 19, 29, 47, 79, 127, 199, 331, 521, 853, 1367, 2207, 3571, 5779, 9349, 15131, 24481, 39607, 64081, 103687, 167771, 271451, 439217, 710663, 1149857, 1860503, 3010349, 4870861, 7881221, 12752053, 20633279, 33385291, 54018521, 87403831

Offset: 0

Michel Lagneau, Nov 02 2012

nonn

			a(6) = 19 because 19 is the smallest prime not less than 18 (the 6th Lucas number).

Cf. A000204, A138185.

Mathematica
```
NextPrime/@(LucasL[Range[0,50]]-1)
```

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A138184 Largest prime not exceeding Fibonacci(n) = A000045(n).

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A138183 Smallest Fibonacci number not less than the n-th prime.

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A375751 a(n) is the difference between F=A000045(n) and the largest prime not exceeding F.

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A218557 Smallest prime >= n-th Lucas number.

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