A074966 -id:A074966 - cp's OEIS frontend

A085752 Duplicate of A074966.

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

Offset: 1

dead

A074967 a(n) = least k such that n^n - k is prime.

1, 4, 5, 4, 7, 2, 3, 10, 33, 42, 19, 12, 17, 52, 59, 18, 65, 2, 51, 2, 23, 120, 35, 2, 63, 10, 39, 186, 7, 74, 47, 200, 53, 24, 19, 48, 333, 56, 57, 192, 127, 348, 63, 124, 213, 60, 359, 2, 213, 2, 387, 526, 269, 252, 863, 16, 131, 370, 503, 294, 83, 68, 317

Offset: 2

Zak Seidov, Oct 03 2002

nonn

Seiichi Manyama, Table of n, a(n) for n = 2..500

Cf. A033933, A074966.

PrimePrevDelta[n_]:=Module[{k},k=n-1;While[ !PrimeQ[k],k-- ];k=n-k]; lst={};Do[AppendTo[lst,PrimePrevDelta[n^n]],{n,2,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 11 2009 *)
lk[n_]:=Module[{nn=n^n},nn-NextPrime[nn,-1]]; Array[lk,70,2] (* Harvey P. Dale, Jan 20 2019 *)

a(n)=(x->x-precprime(x))(n^n) \\ Charles R Greathouse IV, Nov 25 2014

More terms from Robert G. Wilson v, Oct 04 2002

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

A098682 Smallest prime larger than n^n.

Original entry on oeis.org

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

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

Vladimir Joseph Stephan Orlovsky, Jun 11 2009

nonn

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

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

Cf. A074966, A074967.

Cf. A000312, A013633.

for n from 2 to 100 do nn := n^n ; printf("%d,",nextprime(nn)-prevprime(nn) ) ; od: # R. J. Mathar, Jun 12 2009

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 *)

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

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

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,", "))

A300292 Numbers k such that k^k + 9 is a prime.

Original entry on oeis.org

2, 130, 140

Offset: 1

Seiichi Manyama, Mar 16 2018

No more terms <= 7000. - Jon E. Schoenfield, Mar 16 2018

No more terms <= 30000. - Michael S. Branicky, Sep 02 2024

Numbers k such that k^k + b is a prime: A300981 (b=-10), A300976 (b=-5), A100408 (b=-2), A100407 (b=2), A166852 (b=3), A100837 (b=4), A100838 (b=7), this sequence (b=9), A100839 (b=10), A173974 (b=43).

Cf. A074966.

isok(k) = ispseudoprime(k^k + 9); \\ Altug Alkan, Mar 16 2018

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

Farideh Firoozbakht, Mar 04 2005

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

Cf. A103112, A074966, A074967.

a(n)=(x->nextprime(x)-x)(n^n^n) \\ Charles R Greathouse IV, Nov 25 2014

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

Farideh Firoozbakht, Mar 04 2005

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

Cf. A103111, A074967, A074966.

a(n)=(x->x-precprime(x))(n^n^n) \\ Charles R Greathouse IV, Nov 25 2014

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

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)).

cp's OEIS Frontend

A085752 Duplicate of A074966.

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A074967 a(n) = least k such that n^n - k is prime.

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A098682 Smallest prime larger than n^n.

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

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

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A300292 Numbers k such that k^k + 9 is a prime.

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PARI

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

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PARI

Extensions

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

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PARI

Extensions

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

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