A180422 -id:A180422 - cp's OEIS frontend

A075406 a(n) is the number of terms in the sum in A075405 (or 0 if no such square exists).

24, 0, 2, 0, 0, 0, 23, 0, 24, 0, 22898, 0, 96, 0, 97, 0, 23, 11, 0, 2, 96, 59, 0, 0, 24, 0, 33, 50, 0, 169, 0, 578, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 122, 0, 96, 0, 0, 3479, 0, 0, 2075, 0, 33, 0, 0, 0, 242, 218, 0, 50, 0, 0, 0, 0, 0, 122, 36481, 0, 24, 0, 0, 0, 0, 0, 0, 194, 0, 0, 0, 50, 0, 0, 0, 242, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Zak Seidov, Sep 13 2002

nonn

Note that a(n) is either 0 or a number in A001032.

			a(1) = 25 because the sum 1^2+...+24^2 consists of 25 terms, see A075404.

See A180422.

Cf. A000330, A075404, A075405.

s[n_, k_]:=Module[{m=n+k-1}, (m(m+1)(2m+1)-n(n-1)(2n-1))/6]; mx=40000; Table[k=2; While[k

Corrected and extended by Lior Manor, Sep 19 2002

Corrected and edited by T. D. Noe, Jan 21 2011

A182487 Nextprime(F(n)) - prevprime(F(n)), where F(n) is the n-th Fibonacci number.

Original entry on oeis.org

3, 4, 4, 6, 4, 6, 6, 14, 10, 10, 6, 6, 8, 18, 12, 24, 16, 10, 6, 12, 30, 12, 24, 42, 30, 24, 60, 24, 30, 34, 30, 36, 46, 12, 36, 18, 34, 24, 24, 30, 36, 52, 72, 16, 22, 48, 44, 50, 34, 20, 20, 28, 44, 50, 40, 92, 60, 86, 16, 52, 48, 66, 46, 168, 50, 174, 36

Offset: 4

Alex Ratushnyak, May 02 2012

Smallest prime following Fibonacci(n) minus largest prime immediately preceding Fibonacci(n). Starting from Fibonacci(4), because for n<4 there is no prime preceding Fibonacci(n).

			a(0) = A014208(4) - A180422(0) = 5 - 2 = 3,
a(7) = A014208(11) - A180422(7) = 97-83 = 14.

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Cf. A014208, A180422, A013633, A058043, A058054, A161503.

Cf. A079677 (distance from F(n) to the nearest prime).

a:= n-> (f-> nextprime(f)-prevprime(f))(combinat[fibonacci](n)):
seq(a(n), n=4..100);  # Alois P. Heinz, Jul 29 2015

Table[f = Fibonacci[n]; NextPrime[f] - NextPrime[f, -1], {n, 4, 100}] (* T. D. Noe, May 02 2012 *)

a(n) = A014208(n+4) - A180422(n).

A252296 Fibonacci numbers k for which the difference between k and the largest prime less than k is also prime.

Original entry on oeis.org

5, 13, 21, 34, 55, 144, 610, 2584, 6765, 10946, 46368, 196418, 832040, 14930352, 267914296, 1134903170, 4807526976, 365435296162, 1548008755920, 117669030460994, 498454011879264, 2111485077978050, 160500643816367088, 12200160415121876738, 51680708854858323072

Offset: 1

Carlos Eduardo Olivieri, Dec 16 2014

a(n) - p = q, where a(n) is a Fibonacci number, p is the largest prime less than a(n), and q is also prime.

The only terms that are primes are 5 and 13, since there are no other Fibonacci numbers that are twin primes: see the MacKinnon and Gagola link. - Robert Israel, Jan 13 2015

			For n = 1: a(1) = 5, 5 - 3 = 2.
For n = 4: a(4) = 34, 34 - 31 = 3.
For n = 7: a(7) = 610, 610 - 607 = 3.
For n = 11: a(11) = 46368, 46368 - 46351 = 17.

N. MacKinnon and S. M. Gagola, Jr., Fibonacci twin primes (solution to problem 10844), American Mathematical Monthly 109, No. 1 (Jan., 2002), 78.

Cf. A180422, A000045.

select(t -> isprime(t - prevprime(t)), [seq(combinat:-fibonacci(n),n=4..1000)]); # Robert Israel, Dec 16 2014

Select[ Fibonacci@ Range[4, 100], PrimeQ[# - NextPrime[#, -1]] &]

for(n=1,100,f=fibonacci(n);if(f>2&&isprime(f-precprime(f-1)),print1(f,", "))) \\ Derek Orr, Dec 30 2014

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A075406 a(n) is the number of terms in the sum in A075405 (or 0 if no such square exists).

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A182487 Nextprime(F(n)) - prevprime(F(n)), where F(n) is the n-th Fibonacci number.

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A252296 Fibonacci numbers k for which the difference between k and the largest prime less than k is also prime.

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