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 1-8 of 8 results.

A110066 Numbers n such that 10^n - prime(n) is prime.

Original entry on oeis.org

2, 5, 40, 69, 586, 927, 1393, 11411, 32741, 79040
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 12 2005

Keywords

Comments

There is no further term up to 10800.
a(11) > 10^5. - Robert Price, Feb 26 2015

Crossrefs

Programs

  • Mathematica
    Do[If[PrimeQ[10^n - Prime[n]], Print[n]], {n, 10800}]
  • PARI
    is(n)=ispseudoprime(10^n-prime(n)) \\ Charles R Greathouse IV, May 15 2013

Extensions

a(8)-a(10) from Robert Price, Feb 26 2015

A110065 Numbers k such that 10^k - k is prime.

Original entry on oeis.org

3, 23, 171, 903, 9911, 48107, 48449, 60959
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 11 2005

Keywords

Comments

For each n, a(n) == 3 (mod 6) or a(n) == 5 (mod 6).
There is no further term up to 16000. - Farideh Firoozbakht, Dec 02 2006
a(9) > 10^5. - Robert Price, Feb 19 2015

Crossrefs

Programs

  • PARI
    is(n)=isprime(10^n-n) \\ Charles R Greathouse IV, Feb 17 2017
    
  • Python
    from sympy import isprime
    def afind(limit):
      m, pow10 = 0, 1
      while m <= limit:
        if isprime(pow10 - m): print(m, end=", ")
        m, pow10 =  m + 1, pow10 * 10
    afind(1000) # Michael S. Branicky, Mar 23 2021

Extensions

a(5) from Farideh Firoozbakht, Dec 02 2006
Definition corrected by Farideh Firoozbakht, Dec 12 2006
a(6)-a(8) from Robert Price, Feb 19 2015

A174176 Numbers n such that 10^n-2*n+1 is prime.

Original entry on oeis.org

2, 5, 14, 42, 72, 74, 354, 1176, 1274, 4815, 6885, 28214
Offset: 1

Views

Author

Vincenzo Librandi, Mar 11 2010

Keywords

Comments

a(13) > 10^5. - Robert Price, Mar 26 2015

Crossrefs

Programs

  • Magma
    /* The code gives only the terms up to 354: */ [n: n in [1..600] | IsPrime(10^n-2*n+1) ]
    
  • Mathematica
    Select[Range[5000], PrimeQ[(10^# - 2 # + 1)] &] (* Vincenzo Librandi, Oct 05 2012 *)
  • PARI
    is(n)=ispseudoprime(10^n-2*n+1) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

a(8)-a(10) from Vincenzo Librandi, Oct 05 2012
a(11)-a(12) from Robert Price, Mar 26 2015

A174177 Numbers k such that 10^k-2*k-1 is prime.

Original entry on oeis.org

1, 5, 11, 14, 19, 55, 101, 560, 805, 3188, 4441, 25733, 37501
Offset: 1

Views

Author

Vincenzo Librandi, Mar 11 2010

Keywords

Comments

a(14) > 10^5. - Robert Price, Mar 13 2015

Crossrefs

Programs

  • Magma
    [n: n in [1..550] | IsPrime(10^n-2*n-1) ];
    
  • Mathematica
    Select[Range[5000], PrimeQ[(10^# - 2*# - 1)] &] (* Vincenzo Librandi, Oct 05 2012 *)
  • PARI
    for(n=1, 999, ispseudoprime(10^n-2*n-1) && print1(n", "))  \\  M. F. Hasler, Aug 06 2011

Extensions

a(10)-a(11) from Vincenzo Librandi, Oct 05 2012
a(12)-a(13) from Robert Price, Mar 13 2015

A193881 Numbers n such that 10^n-sigma(n^2) is prime.

Original entry on oeis.org

7, 52, 446, 614, 1137, 4852, 5615, 22154, 71291
Offset: 1

Views

Author

M. F. Hasler, Aug 07 2011

Keywords

Comments

sigma(x) is even unless x is a square or twice a square, therefore 10^n-sigma(n) can't be prime unless n is a square or twice a square, and {2, 49} are the only solutions < 10^4.
a(10) > 10^5. - Robert Price, Mar 24 2015

Crossrefs

Programs

  • Magma
    [n: n in [1..450] | IsPrime(10^n-DivisorSigma(1,n^2))]; // Vincenzo Librandi, Mar 26 2015
  • Mathematica
    Select[Range[1000], PrimeQ[10^# - DivisorSigma[1, #^2]] &] (* Robert Price, Mar 24 2015 *)
  • PARI
    for(n=1, 9999, ispseudoprime(t=10^n-sigma(n^2)) && print1(n", "))
    

Extensions

a(6)-a(9) from Robert Price, Mar 25 2015

A193825 Primes of the form 10^n-prime(n).

Original entry on oeis.org

97, 99989, 9999999999999999999999999999999999999827, 999999999999999999999999999999999999999999999999999999999999999999653
Offset: 1

Views

Author

M. F. Hasler, Aug 06 2011

Keywords

Comments

Next term (n=586) is too large to be listed above. See A110066 for the numbers n which yield further terms of this sequence.

Crossrefs

Programs

  • PARI
    for(n=1,999, ispseudoprime(t=10^n-prime(n)) && print1(t","))

Formula

a(n)=10^A110066(n)-prime(A110066(n)).

A193882 Numbers k such that 10^k+sigma(k^2) is prime.

Original entry on oeis.org

1, 2, 3, 8, 13, 15, 19, 20, 41, 47, 50, 76, 100, 162, 204, 310, 318, 536, 2502, 4016, 5612, 5849, 52753, 64843
Offset: 1

Views

Author

M. F. Hasler, Aug 07 2011

Keywords

Comments

sigma(x) is even unless x is a square or twice a square, therefore 10^k+sigma(k) can't be prime unless k is a square or twice a square, and {1, 2, 4, 242} are the only solutions < 5000.
a(25) > 10^5. - Robert Price, May 08 2015

Crossrefs

Programs

  • Mathematica
    Select[Range[0, 1000], PrimeQ[10^# + DivisorSigma[1, #^2]] &] (* Robert Price, May 08 2015 *)
  • PARI
    for(n=1, 9999, ispseudoprime(10^n+sigma(n^2)) && print1(n", "))

Extensions

a(19)-a(24) from Robert Price, May 08 2015

A256451 Numbers n such that 10^n + prime(n) is prime.

Original entry on oeis.org

2, 4, 27, 63, 756, 899, 8088, 15216, 47969, 50943
Offset: 1

Views

Author

Robert Price, Mar 29 2015

Keywords

Comments

a(11) > 10^5. - Robert Price, Mar 29 2015

Examples

			4 is in this sequence since the fourth prime is 7 and 10^4+7=10007 is prime.
		

Crossrefs

Programs

  • Magma
    [n: n in [1..770] | IsPrime(NthPrime(n) + 10^n)]; // Vincenzo Librandi, Mar 30 2015
  • Mathematica
    Select[Range[100000], PrimeQ[10^# + Prime[#]] &]
  • PARI
    for(n=1,10^3,if(ispseudoprime(10^n+prime(n)),print1(n,", "))) \\ Derek Orr, Mar 29 2015
    
Showing 1-8 of 8 results.