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 1-6 of 6 results.

A273598 Numbers k such that (11^k - 6^k)/5 is prime.

Original entry on oeis.org

2, 3, 11, 163, 191, 269, 1381, 1493, 38453
Offset: 1

Views

Author

Tim Johannes Ohrtmann, May 26 2016

Keywords

Comments

All terms are prime.
The corresponding primes: 17, 223, 56989774711, ...

Crossrefs

Programs

  • Mathematica
    Select[Range[1, 10000], PrimeQ[(11^# - 6^#)/5] &]
  • PARI
    for(n=1, 10000, if(isprime((11^n - 6^n)/5), print1(n, ", ")))

Extensions

a(9) from Michael S. Branicky, Nov 10 2024

A273599 Numbers k such that (11^k - 7^k)/4 is prime.

Original entry on oeis.org

5, 19, 67, 107, 593, 757, 1801, 2243, 2383, 6043, 10181, 11383, 15629
Offset: 1

Views

Author

Tim Johannes Ohrtmann, May 26 2016

Keywords

Comments

All terms are prime.
The corresponding primes: 36061, 15286922888307293287, 1483371444025889427763765389467527889556636442659800720575790059738807, ...
a(14) > 50000. - Michael S. Branicky, Nov 11 2024

Crossrefs

Programs

  • Mathematica
    Select[Range[1, 10000], PrimeQ[(11^# - 7^#)/4] &]
  • PARI
    for(n=1, 10000, if(isprime((11^n - 7^n)/4), print1(n, ", ")))

A273600 Numbers k such that (11^k - 8^k)/3 is prime.

Original entry on oeis.org

2, 7, 11, 17, 37, 521, 877, 2423
Offset: 1

Views

Author

Tim Johannes Ohrtmann, May 26 2016

Keywords

Comments

All terms are prime.
The corresponding primes: 19, 5796673, 92240578673, 167731742895202841, 113345629904382710526197539019199125641, ...
a(9) > 50000. - Michael S. Branicky, Nov 11 2024

Crossrefs

Programs

  • Mathematica
    Select[Range[1, 10000], PrimeQ[(11^# - 8^#)/3] &]
  • PARI
    for(n=1, 10000, if(isprime((11^n - 8^n)/3), print1(n, ", ")))

A273601 Numbers k such that (11^k - 9^k)/2 is prime.

Original entry on oeis.org

5, 31, 271, 929, 2789, 4153
Offset: 1

Views

Author

Tim Johannes Ohrtmann, May 26 2016

Keywords

Comments

All terms are prime.
The corresponding primes: 51001, 95780952266636767336259095696501, ...
a(7) > 50000. - Michael S. Branicky, Nov 11 2024

Crossrefs

Programs

  • Mathematica
    Select[Range[1, 10000], PrimeQ[(11^# - 9^#)/2] &]
  • PARI
    for(n=1, 10000, if(isprime((11^n - 9^n)/2), print1(n, ", ")))

A199820 Primes of the form 11^n - 10^n.

Original entry on oeis.org

331, 61051, 51159090448414546291
Offset: 1

Views

Author

Vincenzo Librandi, Nov 21 2011

Keywords

Comments

The next term is too large to include (see A062577).

Crossrefs

Cf. A062577.

Programs

  • Magma
    [ a: n in [0..300] | IsPrime(a) where a is 11^n-10^n ]
  • Mathematica
    Select[11^Range[3000]-10^Range[3000],PrimeQ]

A247093 Triangle read by rows: T(m,n) = smallest odd prime p such that (m^p-n^p)/(m-n) is prime (0

Original entry on oeis.org

3, 3, 3, 0, 0, 3, 3, 5, 13, 3, 3, 0, 0, 0, 5, 5, 3, 3, 5, 3, 3, 3, 0, 3, 0, 19, 0, 7, 0, 3, 0, 0, 3, 0, 3, 7, 19, 0, 3, 0, 0, 0, 31, 0, 3, 17, 5, 3, 3, 5, 3, 5, 7, 5, 3, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 5, 3, 7, 5, 5, 3, 7, 3, 3, 251, 3, 17, 3, 0, 5, 0, 151, 0, 0, 0, 59, 0, 5, 0, 3, 3, 5, 0, 1097, 0, 0, 3, 3, 0, 0, 7, 0, 17, 3
Offset: 1

Views

Author

Eric Chen, Nov 18 2014

Keywords

Comments

T(m,n) is 0 if and only if m and n are not coprime or A052409(m) and A052409(n) are not coprime. (The latter has some exceptions, like T(8,1) = 3. In fact, if p is a prime and does not equal to A052410(gcd(A052409(m),A052409(n))), then (m^p-n^p)/(m-n) is composite, so if it is not 0, then it is A052410(gcd(A052409(m),A052409(n))).) - Eric Chen, Nov 26 2014
a(i) = T(m,n) corresponds only to probable primes for (m,n) = {(15,4), (18,1), (19,18), (31,6), (37,22), (37,25), ...} (i={95, 137, 171, 441, 652, 655, ...}). With the exception of these six (m,n), all corresponding primes up to a(663) are definite primes. - Eric Chen, Nov 26 2014
a(n) is currently known up to n = 663, a(664) = T(37, 34) > 10000. - Eric Chen, Jun 01 2015
For n up to 1000, a(n) is currently unknown only for n = 664, 760, and 868. - Eric Chen, Jun 01 2015

Examples

			Read by rows:
m\n        1   2   3   4   5   6   7   8   9   10  11
2          3
3          3   3
4          0   0   3
5          3   5   13  3
6          3   0   0   0   5
7          5   3   3   5   3   3
8          3   0   3   0   19  0   7
9          0   3   0   0   3   0   3   7
10         19  0   3   0   0   0   31  0   3
11         17  5   3   3   5   3   5   7   5   3
12         3   0   0   0   3   0   3   0   0   0   3
etc.
		

Crossrefs

Cf. A128164 (n,1), A125713 (n+1,n), A125954 (2n+1,2), A122478 (2n+1,2n-1).
Cf. A000043 (2,1), A028491 (3,1), A057468 (3,2), A059801 (4,3), A004061 (5,1), A082182 (5,2), A121877 (5,3), A059802 (5,4), A004062 (6,1), A062572 (6,5), A004063 (7,1), A215487 (7,2), A128024 (7,3), A213073 (7,4), A128344 (7,5), A062573 (7,6), A128025 (8,3), A128345 (8,5), A062574 (8,7), A173718 (9,2), A128346 (9,5), A059803 (9,8), A004023 (10,1), A128026 (10,3), A062576 (10,9), A005808 (11,1), A210506 (11,2), A128027 (11,3), A216181 (11,4), A128347 (11,5), A062577 (11,10), A004064 (12,1), A128348 (12,5), A062578 (12,11).

Programs

  • Mathematica
    t1[n_] := Floor[3/2 + Sqrt[2*n]]
    m[n_] := Floor[(-1 + Sqrt[8*n-7])/2]
    t2[n_] := n-m[n]*(m[n]+1)/2
    b[n_] := GCD @@ Last /@ FactorInteger[n]
    is[m_, n_] := GCD[m, n] == 1 && GCD[b[m], b[n]] == 1
    Do[k=2, If[is[t1[n], t2[n]], While[ !PrimeQ[t1[n]^Prime[k] - t2[n]^Prime[k]], k++]; Print[Prime[k]], Print[0]], {n, 1, 663}] (* Eric Chen, Jun 01 2015 *)
  • PARI
    a052409(n) = my(k=ispower(n)); if(k, k, n>1);
    a(m, n) = {if (gcd(m,n) != 1, return (0)); if (gcd(a052409(m), a052409(n)) != 1, return (0)); forprime(p=3,, if (isprime((m^p-n^p)/(m-n)), return (p)););}
    tabl(nn) = {for (m=2, nn, for(n=1, m-1, print1(a(m,n), ", ");); print(););} \\ Michel Marcus, Nov 19 2014
    
  • PARI
    t1(n)=floor(3/2+sqrt(2*n))
    t2(n)=n-binomial(floor(1/2+sqrt(2*n)), 2)
    b(n)=my(k=ispower(n)); if(k, k, n>1)
    a(n)=if(gcd(t1(n),t2(n)) !=1 || gcd(b(t1(n)), b(t2(n))) !=1, 0, forprime(p=3,2^24,if(ispseudoprime((t1(n)^p-t2(n)^p)/(t1(n)-t2(n))), return(p)))) \\ Eric Chen, Jun 01 2015
Showing 1-6 of 6 results.