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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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

Cf. A005808, A210506, A128027, A216181, A128347, A273598, A273600, A273601, A062577.

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

Cf. A005808, A210506, A128027, A216181, A128347, A273598, A273599, A273601, A062577.

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

Cf. A005808, A210506, A128027, A216181, A128347, A273598, A273599, A273600, A062577.

Programs

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

A128049 Least number k>0 such that abs((3^k - (3-n)^k)/n) is prime, or 0 if no such prime exists.

Original entry on oeis.org

0, 2, 3, 2, 2, 3, 0, 3, 2, 2, 3, 2, 0, 2, 3, 0, 3, 2, 0, 2, 37, 0, 3, 2, 0, 2, 1153, 0, 83, 2, 0, 3, 11, 0, 3, 2, 0, 2, 3, 0, 557, 19, 0, 2, 3, 0, 7, 2, 0, 2, 631, 0, 5, 2, 0, 3, 3, 0, 239, 2, 0, 5, 3, 0, 3, 2, 0, 2, 317, 0, 3, 103, 0, 2, 7, 0, 3, 2, 0, 2, 43
Offset: 0

Views

Author

Alexander Adamchuk, Feb 12 2007

Keywords

Comments

a(-n) = A128033(n).
a(3*n) = 0 except a(3) = a(9) = 2.
All positive terms are primes.

Links

Crossrefs

Cf. A128033 (least number k>0 such that ((n+3)^k - 3^k)/n is prime), A028491 (numbers n such that (3^n - 1)/2 is prime).
Cf. A111010, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • PARI
    a(n) = my(p=3); if(isprime(abs(n-6)), 2, if(n%3, while(!ispseudoprime((3^p-(3-n)^p)/n), p=nextprime(p+1)); p, 0)); \\ Jinyuan Wang, Nov 28 2020

Extensions

Name changed by Jinyuan Wang, Nov 28 2020

A173718 Numbers n such that (9^n - 2^n)/7 is prime.

Original entry on oeis.org

2, 3, 5, 13, 29, 37, 1021, 1399, 2137, 4493, 5521, 108553, 200807
Offset: 1

Views

Author

Robert Price, Dec 22 2012

Keywords

Comments

All terms are prime.
a(14) > 10^6.

Links

Crossrefs

Cf. A004063, A028491, A057468, A059801, A121877, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • Mathematica
    Select[ Prime[ Range[1, 100000] ], PrimeQ[ (9^# - 2^#)/7 ]& ]
  • PARI
    is(n)=ispseudoprime((9^n-2^n)/7) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

a(12)-a(13) from Jon Grantham, Jul 29 2023

A128033 Least number k>0 such that ((n+3)^k - 3^k)/n is prime, or 0 if no such prime exists.

Original entry on oeis.org

0, 2, 13, 0, 3, 2, 0, 2, 3, 0, 7, 2, 0, 2, 3, 0, 73, 2, 0, 5, 3, 0, 3, 2, 0, 2, 3, 0, 3, 3, 0, 2, 5, 0, 3, 2, 0, 2, 401, 0, 3, 2, 0, 5, 5, 0, 3, 2, 0
Offset: 0

Views

Author

Alexander Adamchuk, Feb 11 2007

Keywords

Comments

All positive terms are primes.
a(50)-a(67) = {7, 0, 79, 2, 0, 2, 109, 0, 5, 5, 0, 2, 5, 0, 131, 2, 0, 2}. a(69)-a(121) = {0, 3, 19, 0, 2, 5, 0, 11, 2, 0, 13, 7, 0, 3, 2, 0, 3, 11, 0, 3, 19, 0, 2, 3, 0, 11, 2, 0, 2, 3, 0, 17, 2, 0, 2, 3, 0, 5, 2, 0, 3, 31, 0, 17, 5, 0, 47, 31, 0, 3, 3, 0, 2}.
a(49) > 10000. - Jinyuan Wang, Nov 28 2020

Crossrefs

Cf. A128049 (least number k>0 such that abs((3^k - (3-n)^k)/n) is prime), A028491, A121877, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • PARI
    a(n) = my(p=2); if(n%3, while(!ispseudoprime(((n+3)^p-3^p)/n), p=nextprime(p+1)); p, 0); \\ Jinyuan Wang, Nov 28 2020

Formula

a(3*n) = 0.

A215487 Numbers k such that (7^k - 2^k)/5 is prime.

Original entry on oeis.org

3, 7, 19, 79, 431, 1373, 1801, 2897, 46997, 341063, 508867, 720497, 846913
Offset: 1

Views

Author

Robert Price, Aug 12 2012

Keywords

Comments

All terms are prime.
a(14) > 10^6.

Links

Crossrefs

Cf. A004063, A028491, A057468, A059801, A121877, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

Programs

  • Mathematica
    Select[ Prime[ Range[1, 300] ], PrimeQ[ (7^# - 2^#)/5 ]& ]
  • PARI
    is(n)=ispseudoprime((7^n-2^n)/5) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(10)-a(13) from Jon Grantham, Jul 29 2023

A224691 Numbers n such that (13^n - 4^n)/9 is prime.

Original entry on oeis.org

2, 5, 19, 109, 157, 8521, 26017, 26177
Offset: 1

Views

Author

Robert Price, Apr 15 2013

Keywords

Comments

All terms are prime.
a(9) > 10^5.

Crossrefs

Cf. A004063, A028491, A057468, A059801, A121877, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032, A210506, A128347.

Programs

  • Mathematica
    Select[Prime[Range[1, 100000]], PrimeQ[(13^# - 4^#)/9]&]
  • PARI
    is(n)=ispseudoprime((13^n-4^n)/9) \\ Charles R Greathouse IV, Jun 13 2017

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

A138932 Primes of the form (11^n - 3^n)/8.

Original entry on oeis.org

163, 20101, 7644886305906535603, 23992928119718809985809180625983
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 16 2008

Keywords

Crossrefs

Cf. A128027.

Programs

  • Mathematica
    a={}; Do[p=(11^n-3^n)/8; If[PrimeQ[p], AppendTo[a, p]], {n, 1, 16^2}];a
Previous Showing 21-30 of 33 results. Next

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