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 1-10 of 51 results. Next

A139069 Number of 3's in A020458(n).

Original entry on oeis.org

0, 1, 1, 1, 2, 3, 3, 4, 3, 3, 3, 2, 4, 4, 4, 5, 5, 5, 3, 3, 3, 3, 5, 5, 2, 3, 5, 5, 6, 5, 6, 1, 3, 3, 3, 3, 3, 4, 3, 3, 4, 7, 3, 7, 5, 5, 5, 4, 5, 7, 2, 5, 4, 4, 5, 5, 4, 5, 4, 5, 2, 4, 4, 4, 4, 5, 5, 4, 4, 5, 5, 7, 7, 4, 5, 7, 7, 5, 7, 7, 8, 7, 7, 3, 3, 5, 5, 3, 6, 3, 6, 6, 3, 5, 5, 5, 3, 6, 6
Offset: 1

Views

Author

Paul Curtz, Jun 05 2008

Keywords

Extensions

More terms from Ray Chandler, Aug 06 2008

A069749 Number of primes less than 10^n containing only the digits 2 and 3 (A020458).

Original entry on oeis.org

2, 3, 5, 7, 11, 18, 31, 44, 83, 135, 239, 436, 818, 1436, 2773, 4695, 9244, 17022, 32948, 58158, 116040, 214188, 423902, 791950, 1554834, 2904470, 5725780, 10536383, 21070698, 40748211, 79634658, 148530950, 296094802, 561919901
Offset: 1

Views

Author

Robert G. Wilson v, Apr 22 2002

Keywords

Comments

a(22) / A006880(22) = 214188 / 201467286689315906290 =~ 10^-15. But out of the 2^22 candidates for primes, ~5% are.

Crossrefs

Programs

  • Mathematica
    s = 0; Do[k = 0; While[k < 2^n, k++; If[p = FromDigits[ PadLeft[ IntegerDigits[k, 2], n] + 2]; PrimeQ[p], s++ ]]; Print[s], {n, 1, 22}]
    With[{c=Select[Flatten[Table[FromDigits/@Tuples[{2,3},n],{n,22}]], PrimeQ]}, Table[Count[c,?(#<10^i&)],{i,22}]] (* _Harvey P. Dale, Mar 18 2016 *)
  • Python
    from sympy import isprime
    from itertools import count, islice, product
    def agen(): # generator of terms
        c = 2
        for d in count(2):
            yield c
            for first in product("23", repeat=d-1):
                t = int("".join(first) + "3")
                if isprime(t): c += 1
    print(list(islice(agen(), 20))) # Michael S. Branicky, May 23 2024

Extensions

a(23)-a(27) from Sean A. Irvine, May 17 2024
a(28)-a(34) from Michael S. Branicky, May 22 2024

A139066 Primes of the form (8+k!)/8.

Original entry on oeis.org

631, 45361, 453601, 59875201, 10897286401, 304112751022080001, 3231502092360622080001, 77556050216654929920001, 1105220249217462744317952000001, 332283946848556096005453226376826986289954816000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (8+k!)/8 is prime see A151913.
The next term (a(11)) has 174 digits. - Harvey P. Dale, May 10 2016

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 8)/8], AppendTo[a, (n! + 8)/8]], {n, 1, 50}]; a
    Select[(8+Range[50]!)/8,PrimeQ] (* Harvey P. Dale, May 10 2016 *)
  • PARI
    for(k=4,1e3,if(ispseudoprime(t=k!/8+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139155(A151913(n)). - Amiram Eldar, Oct 14 2024

Extensions

Corrected link to sequence of indexes. - Serge Batalov, Feb 17 2015
a(10) from Harvey P. Dale, May 10 2016

A139068 Primes of the form k!/9 + 1.

Original entry on oeis.org

4481, 611402462201343216650033936533361654773516861440000000001, 234195255375503079690400057633265510581087082006817356924774723468294901747510352675631491470712754833859385753600000000000000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (9+k!)/9 is prime see A137390.

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 9)/9], AppendTo[a, (n! + 9)/9]], {n, 1, 150}]; a
    Select[Range[100]!/9+1,PrimeQ] (* Harvey P. Dale, Aug 17 2017 *)
  • PARI
    for(n=6,1e4,if(ispseudoprime(t=n!/9+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139156(A137390(n)). - Amiram Eldar, Oct 14 2024

A139070 Primes of the form (10+k!)/10.

Original entry on oeis.org

13, 73, 3991681, 47900161, 130767436801, 2585201673888497664001, 40329146112660563558400001, 1376375309122634504631597958158090240000001, 11962222086548019456196316149565771506438373376000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (10+k!)/10 is prime see A139071.

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 10)/10], AppendTo[a, (n! + 10)/10]], {n, 1, 50}]; a
    Select[(Range[50]!+10)/10,PrimeQ] (* Harvey P. Dale, Sep 18 2013 *)
  • PARI
    for(k=5,1e3,if(ispseudoprime(t=k!/10+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139157(A139071(n)). - Amiram Eldar, Oct 14 2024

A139075 Primes p arising in A139074.

Original entry on oeis.org

3, 2, 3, 31, 1009, 2, 5702401, 631
Offset: 1

Views

Author

Artur Jasinski, Apr 08 2008, Apr 21 2008

Keywords

Comments

a(23) = (23+1579!)/23. - Andrew V. Sutherland, Apr 11 2008.
Smallest mother factorial prime p of order n, i.e. smallest prime of the form (p!+n)/n where p is prime.
For smallest daughter factorial prime p of order n see A139074.
For smallest father factorial prime p of order n see A139207.
For smallest son factorial prime p of order n see A139206.
a(9)=26737!/9+1 is a 106758 digit (probable) prime. Easily calculated but too large to enter here a(10)=13, a(11)=566092801, a(12)=11. [Robert Price, Jan 19 2011]

Crossrefs

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! + n)/n], k++ ]; AppendTo[a, Prime[(Prime[k]! + n)/n]], {n, 1, 8}]; a

A032810 Numbers using only digits 2 and 3.

Original entry on oeis.org

2, 3, 22, 23, 32, 33, 222, 223, 232, 233, 322, 323, 332, 333, 2222, 2223, 2232, 2233, 2322, 2323, 2332, 2333, 3222, 3223, 3232, 3233, 3322, 3323, 3332, 3333, 22222, 22223, 22232, 22233, 22322, 22323, 22332, 22333, 23222, 23223
Offset: 1

Views

Author

Keywords

Comments

Identical to A007931 with substitution of digits 2 -> 3, 1 -> 2, i.e., application of the function A048379 or A256079(n) = n + A002275(A055642(n)). - M. F. Hasler, Mar 21 2015

Crossrefs

Cf. A020458, A143967, A248907 (permutation).
Cf. A032804-A032816 (in other bases), A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032834 (digits 3 & 4), A256290 (digits 4 & 5), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9).

Programs

  • Haskell
    a032810 = f 0 . (+ 1) where
       f y 1 = a004086 y
       f y x = f (10 * y + m + 2) x' where (x', m) = divMod x 2
    -- Reinhard Zumkeller, Mar 18 2015
    
  • Magma
    [n: n in [1..24000] | Set(Intseq(n)) subset {2, 3}]; // Vincenzo Librandi, May 27 2012
    
  • Magma
    [n eq 1 select 2 else IsOdd(n) select 10*Self(Floor(n/2))+2 else Self(n-1)+1: n in [1..40]]; // Bruno Berselli, May 27 2012
    
  • Mathematica
    Flatten[Table[FromDigits[#,10]&/@Tuples[{2,3},n],{n,5}]] (* Vincenzo Librandi, May 27 2012 *)
  • PARI
    A032810(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*2 \\ M. F. Hasler, Mar 26 2015
    
  • Python
    def A032810(n): return int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1<<1)//9 # Chai Wah Wu, Jul 15 2023

Formula

a(n) = f(n+1, 0) with f(n, x) = if n=1 then A004086(x) else f(floor(n/2), 10*x + 2 + n mod 2). - Reinhard Zumkeller, Sep 06 2008
a(n) is Theta(n^(log_2 10)); there are about n^(log_10 2) members of this sequence up to n. - Charles R Greathouse IV, Mar 18 2010
a(n) = A007931(n) + A002275(A000523(n+1)). A055642(a(n)) = A000523(n+1). - M. F. Hasler, Mar 21 2015

A139061 Numbers n for which (4+n!)/4 is prime.

Original entry on oeis.org

4, 5, 6, 13, 21, 25, 32, 40, 61, 97, 147, 324, 325, 348, 369, 1290, 1342, 3167, 6612, 8176, 10990
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For primes of the form (4+k!)/4, see A139060.
a(22) > 25000. - Robert Price, Jan 10 2017

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 4)/4], AppendTo[a, n]], {n, 1, 500}]; a
    Select[Range[500],PrimeQ[(4+#!)/4]&]  (* Harvey P. Dale, Mar 24 2011 *)
  • PARI
    for(n=4,1e3,if(ispseudoprime(n!/4+1),print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011

Extensions

More terms from Serge Batalov, Feb 18 2015
a(19) - a(21) from Robert Price, Jan 10 2017

A139063 Numbers k for which (6+k!)/6 is prime.

Original entry on oeis.org

3, 4, 10, 11, 13, 14, 17, 21, 82, 115, 165, 167, 173, 174, 208, 225, 380, 655, 1187, 2000, 2568, 3010, 4542, 8750, 12257, 12601, 24083
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For primes of the form (6+k!)/6, see A139062.
a(28) > 25000. - Robert Price, Nov 20 2016

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 6)/6], AppendTo[a, n]], {n, 1, 500}]; a
  • PARI
    for(k=3,1e3,if(ispseudoprime(k!/6+1),print1(k", "))) \\ Charles R Greathouse IV, Jul 15 2011

Extensions

a(18) and a(19) from Robert Israel, May 19 2014
More terms from Serge Batalov, Feb 18 2015
a(24)-a(27) from Robert Price, Nov 20 2016

A139065 Numbers k for which (7+k!)/7 is prime.

Original entry on oeis.org

11, 15, 16, 25, 35, 59, 64, 68, 82, 121, 149, 238, 584, 912, 3349, 4111, 4324, 15314, 19944, 20658, 22740, 23364
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For primes of the form (7+k!)/7, see A139064.
a(23) > 25000. - Robert Price, Nov 20 2016

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 7)/7], AppendTo[a, n]], {n, 1, 500}]; a
    Select[Range[500],PrimeQ[(7+#!)/7]&] (* Harvey P. Dale, Sep 01 2014 *)
  • PARI
    for(k=7,1e3,if(ispseudoprime(k!/7+1),print1(k", "))) \\ Charles R Greathouse IV, Jul 15 2011

Extensions

More terms from Serge Batalov, Feb 18 2015
a(18)-a(22) from Robert Price, Nov 20 2016
Showing 1-10 of 51 results. Next