A098682 -id:A098682 - cp's OEIS frontend

A097372 Numbers n such that n=(d_1+6)(d_2+6)...*(d_k+6) where d_1 d_2 ... d_k is the decimal expansion of n.

90, 840, 4320, 59400, 60480, 917280, 2419200, 34992000, 3714984000, 460522782720, 896168448000, 2194698240000, 39109522636800, 229419122688000, 239446056960000, 650997662515200, 3954407288832000, 182279345504256000, 883270791696384000, 275333274192936960000

Offset: 1

Farideh Firoozbakht, Sep 21 2004

			90 is in the sequence because 90 = (9+6)*(0+6).

Hiroaki Yamanouchi and Max Alekseyev, Table of n, a(n) for n = 1..29 (contains all terms below 10^100)

Cf. A097371, A098681, A098682.

Cf. A098113, A098114, A097371, A115227.

Do[h=IntegerDigits[n];l=Length[h];If[n==Product[h[[k]]+6, {k, l}], Print[n]], {n, 130000000}]

More terms from Giovanni Resta, Jan 16 2006
a(19)-a(24) from Hiroaki Yamanouchi, Sep 08 2014
a(25)-a(29) from Max Alekseyev, Jan 25 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

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,", "))

A116481 a(n) = n-th prime larger than n^n.

Original entry on oeis.org

2, 7, 37, 271, 3181, 46703, 823621, 16777421, 387420713, 10000000207, 285311671039, 8916100448623, 302875106592719, 11112006825558313, 437893890380859959, 18446744073709552357, 827240261886336765209

Offset: 1

Zak Seidov, Feb 17 2006

nonn

			a(3)=37 because primes larger than 3^3=27 are 29,31,37,41,... and 37 is 3rd prime > 27.

Cf. A098682.

Mathematica
```
Do[Print[Prime[PrimePi[n^n]+n]],{n,12}]
```

{ a(n) = my(p); p=n^n; for(i=1,n,p=nextprime(p+1)); p; } \\ Max Alekseyev, Feb 01 2007

More terms from Jon E. Schoenfield, Sep 07 2006

Further terms from Max Alekseyev, Feb 01 2007

A193813 Least k such that n^n + k + 1 is a prime.

Original entry on oeis.org

0, 0, 1, 0, 11, 6, 3, 42, 9, 18, 61, 34, 15, 26, 27, 12, 73, 106, 17, 90, 31, 86, 13, 94, 95, 42, 67, 134, 119, 18, 57, 6, 57, 62, 53, 30, 41, 114, 9, 156, 109, 12, 3, 402, 121, 456, 533, 36, 17, 30, 225, 252, 19, 192, 101, 176, 391, 44, 193, 256, 101, 78, 453

Offset: 1

Michel Lagneau, Aug 06 2011

nonn

			a(5) = 11 because 5^5 + 11 + 1 = 37 is prime.

Amiram Eldar, Table of n, a(n) for n = 1..500

Cf. A000312, A098682.

a={};Do[k = 0; While[ !PrimeQ[n^n + k + 1], k++ ]; AppendTo[a, k], {n, 1, 100} ];a

a(n) = nextprime(n^n) - n^n - 1; \\ Michel Marcus, Aug 20 2019

a(n) = A098682(n) - n^n -1. - Michel Marcus, Aug 20 2019

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

A097372 Numbers n such that n=(d_1+6)*(d_2+6)*...*(d_k+6) where d_1 d_2 ... d_k is the decimal expansion of n.

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A098681 Largest prime smaller than n^n.

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Mathematica

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

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Maple

PARI

A116481 a(n) = n-th prime larger than n^n.

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Mathematica

PARI

Extensions

A193813 Least k such that n^n + k + 1 is a prime.

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Mathematica

PARI

Formula

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

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Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula

A097372 Numbers n such that n=(d_1+6)(d_2+6)...*(d_k+6) where d_1 d_2 ... d_k is the decimal expansion of n.