A038833 -id:A038833 - cp's OEIS frontend

A099826 Sum of the first 3^n primes.

2, 10, 100, 1264, 15116, 171148, 1864190, 19697700, 203534530, 2067129306, 20706364528, 205144046742, 2014349179358, 19632546354498, 190150622868298, 1831906588192414, 17567504017456404, 167794196312059488, 1597037992049539274

Offset: 0

Robert G. Wilson v, Oct 25 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 0..36 (calculated using Kim Walisch's primesum program)
Cino Hilliard, Sum first 2^n Primes. [Link corrected by Alexey Beshenov, Jan 25 2009] [broken link]
Kim Walisch, Sum of the primes below x (primesum).

Cf. A000040, A000244, A006988, A007504, A038833, A099824, A099825.

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; k = p = 1; s = 0; Do[ While[p = NextPrim[p]; s = s + p; k < 10^n, k++ ]; k++; Print[s], {n, 0, 16}]

a(n) = A007504(A000244(n)). - Amiram Eldar, Jul 01 2024

More terms from Cino Hilliard, Jan 14 2006

A135371 a(n) = prime(3^(n + 1)) - prime(3^n).

Original entry on oeis.org

3, 18, 80, 316, 1124, 3976, 13770, 46398, 155174, 512700, 1679218, 5454768, 17617664, 56578816, 180896064, 576041630, 1827788446, 5781493590, 18236550884, 57379347420, 180130119286, 564319058202, 1764618506934, 5508483994106, 17168384214168, 53431296170784

Offset: 0

Marvin Ray Burns, Dec 09 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 0..35 (calculated from the b-file at A038833)

Cf. A000040, A038833, A110896, A135373.

Table[Prime[3^(n + 1)] - Prime[3^n], {n, 0, 26}]

a(n) = prime(3^(n + 1)) - prime(3^n); \\ Michel Marcus, Nov 15 2020

a(n) = A038833(n+1) - A038833(n). - Jinyuan Wang, Nov 14 2020

a(23)-a(25) from Jinyuan Wang, Nov 14 2020

A105462 The 3^n-th irregular prime.

Original entry on oeis.org

37, 67, 233, 467, 1307, 4637, 15601, 54437, 184279, 616391, 2009011, 6568151, 21341821, 68826689, 220682383, 704456869

Offset: 1

Robert G. Wilson v, Apr 07 2005

Cf. A038833, A105458, A105467.

ip={ the list of irregular primes to 12 million }; Table[ ip[[3^n]], {n, 0, 11}]

a(12) corrected and a(13)-a(17) added by Amiram Eldar, Mar 05 2019

A105467 Number of irregular primes less than or equal to the 3^n-th prime.

Original entry on oeis.org

0, 0, 5, 22, 91, 286, 863, 2577, 7717, 23160, 69939, 209485, 627826, 1881554, 5645226, 16936048

Offset: 1

Robert G. Wilson v, Apr 07 2005

Limit_{n->inf.} a(n)/3^n = 1-e^(-1/2).

Cf. A038833, A105458, A105462.

ip={ the list of irregular primes to 12 million }; Table[ Length[ Select[ip, # < Prime[3^n] &]], {n, 9}]

Terms corrected and a(10)-a(16) added by Amiram Eldar, Mar 05 2019

A074382 Difference between (1+3^n)-th and (3^n)-th primes.

Original entry on oeis.org

1, 2, 6, 4, 2, 6, 2, 12, 12, 12, 30, 18, 24, 10, 14, 32, 22, 12, 14, 10, 6, 12, 30, 44, 40, 54, 28, 8, 24, 26, 6, 8, 28, 48, 12, 158, 20

Offset: 0

Labos Elemer, Aug 22 2002

			n=25: a(25)=54 because the 847288609443rd prime is 25270000074757 and the 847288609444th prime is 25270000074811.

Cf. A074325, A038833.

NextPrime[#]-#&/@Table[Prime[3^n],{n,25}] (* Harvey P. Dale, Sep 29 2015 *)

a(n) = prime(1+3^n) - prime(3^n).

Corrected by Harvey P. Dale, Sep 29 2015

a(0), a(26)-a(36) from Chai Wah Wu, Aug 30 2019

A074383 Difference between (1+10^n)-th and (10^n)-th primes.

Original entry on oeis.org

1, 2, 6, 8, 14, 12, 4, 18, 8, 24, 6, 42, 18, 48, 60, 52, 48, 8, 22, 20, 60, 38, 54, 48, 58

Offset: 0

Labos Elemer, Aug 22 2002

			a(18)=22 because the (10^18)th prime is 44211790234832169331, the (1+10^18)th prime is 44211790234832169353.

Cf. A006988, A074325, A038833, A074382.

a(n) = prime(1+10^n) - prime(10^n).

a(n) = A151800(A006988(n)) - A006988(n).

a(19) from Max Alekseyev, May 08 2009
a(20)-a(22) from Max Alekseyev, Dec 04 2014
a(23)-a(24) from Chai Wah Wu using the terms in A006988, Sep 18 2018

A095120 a(n) = prime(3^n - 1).

Original entry on oeis.org

3, 19, 101, 409, 1531, 5507, 19273, 65677, 220859, 733559, 2412763, 7867543, 25485179, 82064011, 262960069, 839001707, 2666790157, 8448283721, 26684834629, 84064182049, 264194301341, 828513359543, 2593131866471, 8101615860581, 25270000074743

Offset: 1

Cino Hilliard, Jun 19 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..36 (calculated using the b-file at A038833)

Cf. A038833, A151799.

Prime[3^Range[25]-1] (* Harvey P. Dale, Dec 01 2018 *)

f(n) = for(x=1,n,print1(prime(3^x-1)","))

a(n) = A151799(A038833(n)). - Amiram Eldar, Jul 01 2024

More terms from Harvey P. Dale, Dec 01 2018

A347000 The (m^n)-th prime, written as square array T(n,m) read by falling antidiagonals.

Original entry on oeis.org

2, 3, 2, 5, 7, 2, 7, 23, 19, 2, 11, 53, 103, 53, 2, 13, 97, 311, 419, 131, 2, 17, 151, 691, 1619, 1543, 311, 2, 19, 227, 1321, 4637, 8161, 5519, 719, 2, 23, 311, 2309, 10627, 28687, 38873, 19289, 1619, 2, 29, 419, 3671, 21391, 79349, 171529, 180503, 65687, 3671, 2

Offset: 1

Hugo Pfoertner, Aug 10 2021

			The array begins
  2   3     5      7     11      13       17 ...
  2   7    23     53     97     151      227 ...
  2  19   103    311    691    1321     2309 ...
  2  53   419   1619   4637   10627    21391 ...
  2 131  1543   8161  28687   79349   185707 ...
  2 311  5519  38873 171529  567871  1549817 ...
  2 719 19289 180503 994837 3950183 12579617 ...

Hugo Pfoertner, Table of k, a(k) for k = 1..351, antidiagonals for m+n<=26, flattened.

Cf. A000040, A033844, A038833, A119772, A011757, A055875, A109791, A062448.

Cf. A003320, A051129.

T[n_,m_]:=Prime[m^n];Flatten[Table[Reverse[Table[T[n-m+1,m],{m,n}]],{n,10}]] (* Stefano Spezia, Aug 10 2021 *)

A096324 a(n) = prime(3^prime(n)).

Original entry on oeis.org

23, 103, 1543, 19289, 2412779, 25485211, 2666790167, 26684834641, 2593131866483, 2358539553316997, 22624672879215149

Offset: 1

Cino Hilliard, Aug 02 2004

			a(1) = prime(3^prime(1)) = prime(3^2) = prime(9) = 23.

Subsequence of A038833.

Table[ Prime[ 3^Prime[n]], {n, 9}] (* Robert G. Wilson v, Aug 07 2004 *)

a(n)=prime(3^prime(n)) \\ Charles R Greathouse IV, Nov 02 2014

a(n) = A038833(A000040(n)). - Amiram Eldar, Jul 01 2024

Edited and extended by Robert G. Wilson v, Aug 07 2004

a(10)-a(11) from Charles R Greathouse IV, Nov 02 2014

A119774 (9^n)-th prime.

Original entry on oeis.org

2, 23, 419, 5519, 65687, 733561, 7867547, 82064027, 839001721, 8448283757, 84064182061, 828513359549, 8101615860589, 78701296245541, 760254097357847, 7308703331126371, 69967771422585271, 667349537482051157, 6344383023407982563

Offset: 0

Jim Snow (jsnow(AT)mitre.org), Jun 22 2006

Andrew Booker, The Nth Prime Page.

Cf. A038833.

a[n_] := Prime[9^n]; Array[a, 16, 0] (* Amiram Eldar, Jul 18 2025 *)

a(n)=prime(9^n) \\ Charles R Greathouse IV, Nov 02 2014

a(n) = A038833(2*n). - Amiram Eldar, Jul 18 2025

a(13)-a(18) from Charles R Greathouse IV, Nov 02 2014

cp's OEIS Frontend

A099826 Sum of the first 3^n primes.

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A135371 a(n) = prime(3^(n + 1)) - prime(3^n).

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A105462 The 3^n-th irregular prime.

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A105467 Number of irregular primes less than or equal to the 3^n-th prime.

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A074382 Difference between (1+3^n)-th and (3^n)-th primes.

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A074383 Difference between (1+10^n)-th and (10^n)-th primes.

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A095120 a(n) = prime(3^n - 1).

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A347000 The (m^n)-th prime, written as square array T(n,m) read by falling antidiagonals.

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A096324 a(n) = prime(3^prime(n)).

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