A098681 -id:A098681 - 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

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

A097371 Numbers n such that n=(d_1+5)(d_2+5)...(d_k+5), where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

50, 210, 450, 780, 1500, 3920, 16500, 91728, 269500, 493920, 1293600, 266378112, 317447424, 1277337600, 14948388000, 48697248600, 379748636467200

Offset: 1

Farideh Firoozbakht, Sep 20 2004

All terms are even.

No other terms below 10^100. - Max Alekseyev, Jan 26 2015

			317447424 is in the sequence because 317447424=(3+5)(1+5)(7+5)(4+5)(4+5)(7+5)(4+5)(2+5)(4+5).

Cf. A097372, A098681.

Do[h=IntegerDigits[n];l=Length[h];If[n==Product[h[[k]]+5, {k, l}], Print[n]], {n, 800000000}]

4 more terms from Giovanni Resta, Jan 13 2006

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,", "))

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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A098682 Smallest prime larger than n^n.

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Magma

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A097371 Numbers n such that n=(d_1+5)(d_2+5)*...*(d_k+5), where d_1 d_2 ... d_k is the decimal expansion of n.

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

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Maple

PARI

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

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Author

Keywords

Examples

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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.

A097371 Numbers n such that n=(d_1+5)(d_2+5)...(d_k+5), where d_1 d_2 ... d_k is the decimal expansion of n.