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.

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A062652 Numbers k such that 86^k - 85^k is prime.

Original entry on oeis.org

5, 11, 103, 227, 1637, 9677, 41597
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms greater than 1000 are often only strong pseudoprimes.
All terms are prime. - Robert Price, Apr 14 2014
a(8) > 10^5. - Robert Price, Apr 14 2015

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062666, A215536 (primes 87^n - 86^n).

Programs

  • Mathematica
    Select[Range[0, 300], If[PrimeQ[#], PrimeQ[86^# - 85^#]] &] (* Robert Price, Apr 14 2015 *)
  • PARI
    is(n)=ispseudoprime(86^n-85^n) \\ Charles R Greathouse IV, Jun 12 2017

Extensions

a(7) from Robert Price (computer run by Adam Marciniec), Apr 14 2015

A062655 Numbers k such that 89^k - 88^k is prime.

Original entry on oeis.org

3, 5, 997, 4253, 52511, 59221
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms greater than 1000 are often only strong pseudoprimes.
a(7) > 10^5. - Robert Price, Jun 16 2015

Crossrefs

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

Programs

Extensions

a(5)-a(6) from Robert Price (computer run by Adam Marciniec), Jun 16 2015

A062665 Numbers k such that 99^k - 98^k is prime.

Original entry on oeis.org

2, 709
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

a(3) > 20000. - Derek Orr, Sep 03 2014
Terms must be prime. - Derek Orr, Sep 03 2014
a(3) > 10^5. - Robert Price, Mar 22 2015

Crossrefs

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

Programs

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

A062580 Numbers k such that 14^k - 13^k is prime.

Original entry on oeis.org

3, 11, 83, 461, 659, 1129, 3797, 83869
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms greater than 1000 may correspond to (unproven) strong pseudoprimes.

Crossrefs

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

Programs

Extensions

83869 found from Jean-Louis Charton, Sep 02 2009
Edited by M. F. Hasler, Sep 16 2013

A062594 Numbers k such that 28^k - 27^k is prime.

Original entry on oeis.org

3, 5, 19, 31, 257, 773
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms > 1000 are often only strong pseudoprimes.
a(7) > 10^5. - Robert Price, Sep 04 2012

Crossrefs

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

Programs

A062595 Numbers k such that 29^k - 28^k is prime.

Original entry on oeis.org

3, 7219, 34871
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms > 1000 are often only strong pseudoprimes.
a(4) > 10^5. - Robert Price, Sep 22 2012

Crossrefs

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

Programs

Extensions

a(3) from Robert Price, Sep 22 2012

A062596 Numbers k such that 30^k - 29^k is prime.

Original entry on oeis.org

2, 149, 283, 853, 1741, 4831, 8867
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms > 1000 are often only strong pseudoprimes.
a(8) > 10^5. - Robert Price, Oct 23 2012

Crossrefs

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

Programs

A062597 Numbers k such that 31^k - 30^k is prime.

Original entry on oeis.org

2, 3, 5, 211
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms > 1000 are often only strong pseudoprimes.
a(5) > 10^5 - Robert Price, Nov 14 2012

Crossrefs

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

Programs

A062598 Numbers k such that 32^k - 31^k is prime.

Original entry on oeis.org

5, 1427, 2357, 24499
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms > 1000 often correspond only to strong pseudoprimes.
a(5) > 10^5. - Robert Price, Oct 03 2012

Crossrefs

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

Programs

Extensions

a(4) from Robert Price, Oct 03 2012
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