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 1-4 of 4 results.

A274677 Numbers k such that 7*10^k + 19 is prime.

Original entry on oeis.org

1, 2, 3, 4, 27, 32, 63, 69, 107, 145, 154, 173, 190, 271, 412, 1219, 1509, 2392, 4444, 5567, 7424, 32174, 51573
Offset: 1

Views

Author

Vincenzo Librandi, Jul 04 2016

Keywords

Comments

No term is divisible by 6 (A047253) because 7*1000000^k + 19 = 7*(76923*13 + 1)^k + 19 is divisible by 13 and is therefore not prime. - Bruno Berselli, Jul 05 2016

Examples

			3 is in this sequence because 7*10^3 + 19 = 7019 is prime.
5 is not in the sequence because 7*10^5 + 19 = 79*8861.
Initial terms and associated primes:
a(1) = 1: 89;
a(2) = 2: 719;
a(3) = 3: 7019;
a(4) = 4: 70019, etc.
		

Crossrefs

Subsequence of A047253.
Cf. similar sequences listed in A274676.

Programs

  • Magma
    [n: n in [1..800] | IsPrime(7*10^n+19)];
    
  • Mathematica
    Select[Range[0, 3000], PrimeQ[7 10^# + 19] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+19), print1(n, ", "))); \\ Altug Alkan, Jul 05 2016
    
  • Python
    from sympy import isprime
    def afind(limit, startk=0):
        sevenpow10 = 7*10**startk
        for k in range(startk, limit+1):
            if isprime(sevenpow10 + 19):
                print(k, end=", ")
            k += 1
            sevenpow10 *= 10
    afind(500) # Michael S. Branicky, Dec 31 2021

Extensions

a(20)-a(21) from Michael S. Branicky, Dec 31 2021
a(22)-a(23) from Kamada data by Tyler Busby, Apr 14 2024

A274678 Numbers k such that 7*10^k + 27 is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 34, 38, 49, 51, 89, 91, 132, 227, 3662, 5019, 9729, 25437, 99944, 106553, 114577
Offset: 1

Views

Author

Vincenzo Librandi, Jul 04 2016

Keywords

Examples

			3 is in this sequence because 7*10^3 + 27 = 7027 is prime.
4 is not in the sequence because 7*10^4 + 27 = 70027 = 239 * 293.
Initial terms and associated primes:
a(1) = 1: 97;
a(2) = 2: 727;
a(3) = 3: 7027;
a(4) = 5: 700027, etc.
		

Crossrefs

Cf. similar sequences listed in A274676.

Programs

  • Magma
    [n: n in [1..800] | IsPrime(7*10^n+27)];
    
  • Mathematica
    Select[Range[0, 3000], PrimeQ[7 10^# + 27] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+27), print1(n, ", "))); \\ Altug Alkan, Jul 05 2016
    
  • Python
    from sympy import isprime
    def afind(limit, startk=0):
        sevenpow10 = 7*10**startk
        for k in range(startk, limit+1):
            if isprime(sevenpow10 + 27):
                print(k, end=", ")
            k += 1
            sevenpow10 *= 10
    afind(500) # Michael S. Branicky, Dec 31 2021

Extensions

a(15)-a(16) from Michael S. Branicky, Dec 31 2021
a(17)-a(20) from Kamada data by Tyler Busby, Apr 14 2024

A274679 Numbers k such that 7*10^k + 33 is prime.

Original entry on oeis.org

1, 2, 6, 10, 17, 29, 53, 107, 133, 596, 852, 1068, 1186, 1356, 1673, 1987, 3170, 3312, 5819, 6655, 19267, 20009, 29302, 72614, 170348, 178566
Offset: 1

Views

Author

Vincenzo Librandi, Jul 04 2016

Keywords

Examples

			2 is in this sequence because 7*10^2 + 33 = 733 is prime.
4 is not in the sequence because 7*10^4 + 33 = 70033 = 59 * 1187.
Initial terms and associated primes:
a(1) = 1: 103;
a(2) = 2: 733;
a(3) = 6: 7000033;
a(4) = 10: 70000000033, etc.
		

Crossrefs

Cf. similar sequences listed in A274676.

Programs

  • Magma
    [n: n in [1..500] | IsPrime(7*10^n+33)];
    
  • Mathematica
    Select[Range[0, 3000], PrimeQ[7 10^# + 33] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+33), print1(n, ", "))); \\ Altug Alkan, Jul 05 2016

Extensions

a(19)-a(20) from Michael S. Branicky, Aug 16 2021
a(21)-a(26) from Kamada data by Tyler Busby, Apr 14 2024

A274700 Numbers k such that 7*10^k + 37 is prime.

Original entry on oeis.org

1, 7, 15, 21, 91, 325, 465, 853, 76717
Offset: 1

Views

Author

Vincenzo Librandi, Jul 04 2016

Keywords

Comments

All terms are odd because 7*(9*11+1)^n + 37 is divisible by 11.
a(10) > 10^5. - Michael S. Branicky, Apr 30 2025

Examples

			1 is in this sequence because 7*10 + 37 = 107 is prime.
3 is not in the sequence because 7*10^3 + 37 = 31*227.
Initial terms and associated primes:
  a(1) =  1: 107;
  a(2) =  7: 70000037;
  a(3) = 15: 7000000000000037;
  a(4) = 21: 7000000000000000000037;
  etc.
		

Crossrefs

Cf. similar sequences listed in A274676.

Programs

  • Magma
    [n: n in [1..400] | IsPrime(7*10^n+37)];
    
  • Mathematica
    Select[Range[0, 3000], PrimeQ[7 10^# + 37] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+37), print1(n, ", "))); \\ Altug Alkan, Jul 05 2016

Extensions

Edited by Bruno Berselli, Jul 05 2016
a(9) from Michael S. Branicky, Apr 28 2025
Showing 1-4 of 4 results.