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 1-7 of 7 results.

A074966 a(n) = least k such that n^n + k is prime.

Original entry on oeis.org

1, 1, 2, 1, 12, 7, 4, 43, 10, 19, 62, 35, 16, 27, 28, 13, 74, 107, 18, 91, 32, 87, 14, 95, 96, 43, 68, 135, 120, 19, 58, 7, 58, 63, 54, 31, 42, 115, 10, 157, 110, 13, 4, 403, 122, 457, 534, 37, 18, 31, 226, 253, 20, 193, 102, 177, 392, 45, 194, 257, 102, 79, 454, 231, 306
Offset: 1

Views

Author

Zak Seidov, Oct 03 2002

Keywords

Comments

"Are there any n except 1, 2 and 4 that make n^n + 1 a prime? He [Sierpiński] has shown that if such a prime exists it is greater than 10^30000." - Ogilvy and Anderson

References

  • C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory. Dover. New York: 1988. Page 82.

Links

Crossrefs

Cf. A055385, A074967.

Programs

Extensions

More terms from Robert G. Wilson v, Oct 04 2002
Name taken from Comments section by Jon E. Schoenfield, Jan 14 2015

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

Views

Author

Olaf Voß, Oct 27 2004

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)

A161503 a(n) = NextPrime(n^n) - PrevPrime(n^n).

Original entry on oeis.org

2, 6, 6, 16, 14, 6, 46, 20, 52, 104, 54, 28, 44, 80, 72, 92, 172, 20, 142, 34, 110, 134, 130, 98, 106, 78, 174, 306, 26, 132, 54, 258, 116, 78, 50, 90, 448, 66, 214, 302, 140, 352, 466, 246, 670, 594, 396, 20, 244, 228, 640, 546, 462, 354, 1040, 408, 176, 564, 760
Offset: 2

Views

Author

Vladimir Joseph Stephan Orlovsky, Jun 11 2009

Keywords

Examples

			3 <- 2^2 -> 5; 5 - 3 = 2;
23 <- 3^3 -> 29; 29 - 23 = 6.

Links

Crossrefs

Cf. A074966, A074967.
Cf. A000312, A013633.

Programs

  • Maple
    for n from 2 to 100 do nn := n^n ; printf("%d,",nextprime(nn)-prevprime(nn) ) ; od: # R. J. Mathar, Jun 12 2009
  • Mathematica
    PrimeNext[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k]; PrimePrev[n_]:=Module[{k}, k=n-1;While[ !PrimeQ[k],k-- ];k]; DeltaY[n_]:=PrimeNext[n]-PrimePrev[n]; lst={};Do[AppendTo[lst,DeltaY[n^n]],{n,2,5!}];lst
npnn[n_]:=Module[{nn=n^n},NextPrime[nn]-NextPrime[nn,-1]]; Array[npnn,60,2] (* Harvey P. Dale, Dec 07 2013 *)

Formula

a(n) = A074966(n) + A074967(n) = A013633(A000312(n)). - R. J. Mathar, Jun 12 2009

Extensions

Offset changed by R. J. Mathar, Jun 12 2009

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

Views

Author

Hugo Pfoertner, Mar 10 2020

Keywords

Examples

			   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

Links

Crossrefs

Cf. A000312, A074966, A074967, A098681, A098682, A161503.
Cf. A333185 (position of terms = 0).

Programs

  • Maple
    a:= n-> (m-> m-(prevprime(m)+nextprime(m))/2)(n^n):
seq(a(n), n=2..65);  # Alois P. Heinz, Mar 10 2020
  • PARI
    for(n=2,61, my(f=n^n); print1(f-(precprime(f)+nextprime(f))/2,", "))

A103111 Smallest natural number m such that n^n^n + m is prime.

Original entry on oeis.org

1, 1, 16, 75, 2994, 96545
Offset: 1

Views

Author

Farideh Firoozbakht, Mar 04 2005

Keywords

Examples

			a(5)=2994 because 5^5^5 + 2994 is prime and 5^5^5 + k is composite for 0<k<2994.

Crossrefs

Cf. A103112, A074966, A074967.

Programs

Extensions

a(6) from Donovan Johnson, Mar 06 2008

A103112 Smallest natural number m such that n^n^n - m is a prime.

Original entry on oeis.org

3, 26, 569, 10978, 106843
Offset: 2

Views

Author

Farideh Firoozbakht, Mar 04 2005

Keywords

Examples

			a(5)=10978 because 5^5^5 - 10978 is a prime and 5^5^5 - k is composite for 0<k<10978.

Crossrefs

Cf. A103111, A074967, A074966.

Programs

Extensions

a(6) from Donovan Johnson, Mar 06 2008

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

Views

Author

Hugo Pfoertner, Mar 11 2020

Keywords

Examples

			          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

Crossrefs

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

Programs

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

Formula

A333184(a(n)) = 0.
A074966(a(n)) = A074967(a(n)).
Showing 1-7 of 7 results.

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

Content is available under The OEIS End-User License Agreement.