A161503 -id:A161503 - cp's OEIS frontend

A098682 Smallest prime larger than n^n.

2, 5, 29, 257, 3137, 46663, 823547, 16777259, 387420499, 10000000019, 285311670673, 8916100448291, 302875106592269, 11112006825558043, 437893890380859403, 18446744073709551629, 827240261886336764251, 39346408075296537575531, 1978419655660313589123997

Offset: 1

Olaf Voß, Oct 27 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..386 (terms 1..200 from Vincenzo Librandi)

Cf. A000312 (n^n), A074966, A098681, A116481, A161503, A333184.

[NextPrime(n^n): n in [1..20]]; // Vincenzo Librandi, Sep 04 2017

Table[NextPrime[n^n], {n, 20}] (* Vincenzo Librandi, Sep 04 2017 *)

a(n) = nextprime(n^n); \\ Michel Marcus, Aug 20 2019

a(n) = A074966(n) + n^n. - Michel Marcus, Mar 11 2020

A098681 Largest prime smaller than n^n.

Original entry on oeis.org

3, 23, 251, 3121, 46649, 823541, 16777213, 387420479, 9999999967, 285311670569, 8916100448237, 302875106592241, 11112006825557999, 437893890380859323, 18446744073709551557, 827240261886336764159, 39346408075296537575359

Offset: 2

Olaf Voß, Oct 27 2004

Hugo Pfoertner, Table of n, a(n) for n = 2..386

Cf. A000312, A074967, A098682, A161503, A333184.

PrimePrev[n_]:=Module[{k},k=n-1;While[ !PrimeQ[k],k-- ];k];f[n_]:=n^n;lst={};Do[AppendTo[lst,PrimePrev[f[n]]],{n,30}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)
Table[NextPrime[n^n,-1],{n,2,20}] (* Harvey P. Dale, Dec 02 2017 *)

A333184 a(n) = n^n - (PrevPrime(n^n) + NextPrime(n^n)) / 2.

Original entry on oeis.org

0, 1, 2, -4, 0, -1, -20, 0, 7, -10, -8, -2, -5, 12, 23, -28, -21, -8, -20, -15, -32, 53, -30, -47, 10, -29, -48, 33, -6, 8, 20, 71, -5, -15, -6, 3, 109, 23, -50, 41, 57, 172, -170, 1, -122, -237, 161, -8, 91, -112, 67, 253, 38, 75, 343, -188, 43, 88, 123, 96

Offset: 2

Hugo Pfoertner, Mar 10 2020

sign

			   n Previous P      n^n       Next P    a(n)
     A098681(n)  A000312(n)  A098682(n)
   2          3           4           5   0
   3         23          27          29   1
   4        251         256         257   2
   5       3121        3125        3137  -4
   6      46649       46656       46663   0
   7     823541      823543      823547  -1
   8   16777213    16777216    16777259 -20
   9  387420479   387420489   387420499   0
  10 9999999967 10000000000 10000000019   7

Hugo Pfoertner, Table of n, a(n) for n = 2..1000

Cf. A000312, A074966, A074967, A098681, A098682, A161503.

Cf. A333185 (position of terms = 0).

a:= n-> (m-> m-(prevprime(m)+nextprime(m))/2)(n^n):
seq(a(n), n=2..65);  # Alois P. Heinz, Mar 10 2020

for(n=2,61, my(f=n^n); print1(f-(precprime(f)+nextprime(f))/2,", "))

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).

A333185 Numbers k such that k^k is the average of its nearest 2 primes.

Original entry on oeis.org

2, 6, 9, 940

Offset: 1

Hugo Pfoertner, Mar 11 2020

			          Previous P         k^k           Next P
  a(n)  A098681(a(n))  A000312(a(n))  A098682(a(n))
    2               3              4              5
    6           46649          46656          46663
    9       387420479      387420489      387420499
  940    940^940-3063        940^940   940^940+3063

Cf. A000312, A074966, A074967, A098681, A098682, A161503, A333184.

isok(k) = if (k>1, my(x=k^k); precprime(x-1)+nextprime(x+1) == 2*x); \\ Michel Marcus, Mar 14 2020

A333184(a(n)) = 0.

A074966(a(n)) = A074967(a(n)).

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A098682 Smallest prime larger than n^n.

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A098681 Largest prime smaller than n^n.

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A333184 a(n) = n^n - (PrevPrime(n^n) + NextPrime(n^n)) / 2.

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

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A333185 Numbers k such that k^k is the average of its nearest 2 primes.

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