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 1-5 of 5 results.

A059803 Numbers n such that 9^n - 8^n is prime or a strong pseudoprime.

Original entry on oeis.org

2, 7, 29, 31, 67, 149, 401, 2531, 19913, 30773, 53857, 170099
Offset: 1

Views

Author

Mike Oakes, Feb 23 2001

Keywords

Comments

Some of the larger entries may only correspond to probable primes.
In general, for any positive integers n, a and b, a>b, a necessary condition for a^n-b^n to be prime is that either a-b=1 and n be a prime or n=1 and a-b be prime (from Arturo Magidin and Hagman in Sci.Math, Sep 11, 2010). - Vincenzo Librandi, Sep 12 2010

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062574, A062576-A062666.

Programs

Extensions

Three more terms found by Jean-Louis Charton in 2004-2005: a(9) = 30773, a(10) = 53857, a(11) = 170099. - Alexander Adamchuk, Dec 08 2006

A087895 Primes p such that 10^p - 9^p is composite.

Original entry on oeis.org

5, 13, 17, 23, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293
Offset: 1

Views

Author

Cino Hilliard, Oct 26 2003

Keywords

Crossrefs

Cf. A016189, A062576.
Primes k such that x^k - (x-1)^k is composite: A087489 (x=3), A087490 (x=4), A087685 (x=5), A087749 (x=6), A087759 (x=7), A087763 (x=8), A087894 (x=9), this sequence (x=10).

Programs

  • Mathematica
    Select[Prime[Range[100]],!PrimeQ[10^#-9^#]&] (* Harvey P. Dale, Jun 21 2012 *)
  • PARI
    apmb(a,b,n) = { forprime(x=2,n, y=a^x-b^x; if(!ispseudoprime(y), print1(x","); ) ) }

Extensions

Offset corrected by Mohammed Yaseen, Jul 19 2022

A199819 Primes of the form 10^k-9^k.

Original entry on oeis.org

19, 271, 5217031, 68618940391, 8649148282327007911, 95289871302753755165078396311
Offset: 1

Views

Author

Vincenzo Librandi, Nov 21 2011

Keywords

Links

Crossrefs

Cf. A016189, A062576

Programs

  • Magma
    [ a: n in [0..400] | IsPrime(a) where a is 10^n-9^n ];
  • Mathematica
    Select[10^Range[3000]-9^Range[3000],PrimeQ]

Formula

a(n) = A016189(A062576(n)). - Michel Marcus, Apr 21 2025

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.

Links

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

A273403 Numbers k such that (10^k - 7^k)/3 is prime.

Original entry on oeis.org

2, 31, 103, 617, 10253, 10691, 35353, 129587, 556441
Offset: 1

Views

Author

Tim Johannes Ohrtmann, May 21 2016

Keywords

Comments

All terms are prime.
The corresponding primes: 17, 3333280741539321718064461652419, ...

Links

Crossrefs

Cf. A004023, A128026, A062576.

Programs

  • Mathematica
    Select[Range[1, 10000], PrimeQ[(10^# - 7^#)/3] &]
  • PARI
    for(n=1, 10000, if(isprime((10^n - 7^n)/3), print1(n, ", ")))

Extensions

a(7)-a(9) from Jon Grantham, Jul 29 2023
Showing 1-5 of 5 results.

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