A005808 -id:A005808 - cp's OEIS frontend

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

5, 31, 271, 929, 2789, 4153

Offset: 1

Tim Johannes Ohrtmann, May 26 2016

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

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

Select[Range[1, 10000], PrimeQ[(11^# - 9^#)/2] &]

for(n=1, 10000, if(isprime((11^n - 9^n)/2), print1(n, ", ")))

A141824 Antidiagonals of table A047888 (which counts longest increasing subsequences and pattern avoidances).

Original entry on oeis.org

1, 2, 4, 9, 24, 75, 269, 1095, 5039, 26084, 150356, 952526, 6553011, 48553418, 385693800, 3277413802, 29741002168, 287555932433, 2952769116993, 32079033571080, 367336668735826, 4419518218479215, 55733223965845539, 735448682261126767, 10142738983005750681

Offset: 1

Alford Arnold, Jul 08 2008

nonn

Note that:
A000108 avoids string "123"
A005808 avoids string "1234"
A047889 avoids string "12345"
Note also that the left half and central diagonal of A047888 are partial sums of table A047874.

			We can write A141824(n) = 1 2 4 9 24 ... because A047888 begins
  1;
  1,  1;
  1,  2,  1;
  1,  5,  2,  1;
  1, 14,  6,  2,  1;
etc.

Cf. A000108 (Catalan numbers), A005808, A047889, A047874.

a(12)-a(25) from Alois P. Heinz, Apr 10 2012

A245442 Numbers n such that (50^n - 1)/49 is prime.

Original entry on oeis.org

3, 5, 127, 139, 347, 661, 2203, 6521, 210319

Offset: 1

Robert Price, Jul 22 2014

a(9) > 10^5.

All terms are prime.

Harvey Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
Henri Lifchitz, Mersenne and Fermat primes field

Cf. A028491, A004061, A004062, A004063, A004023, A005808, A004064, A016054, A006032, A006033, A006034, A006035, A127995, A127996, A127997, A127998, A127999, A098438, A128002, A128003, A128004, A128005, A240765, A242797, A243279, A245237.

A245442:=n->`if`(isprime((50^n - 1)/49), n, NULL); seq(A245442(n), n=1..100000); # Wesley Ivan Hurt, Apr 12 2014

Select[Prime[Range[100000]], PrimeQ[(50^# - 1)/49] &]

is(n)=ispseudoprime((50^n-1)/49) \\ Charles R Greathouse IV, Jun 13 2017

a(9)=210319 corresponds to a probable prime discovered by Paul Bourdelais, Aug 04 2020

A181987 Numbers n such that (39^n - 1)/38 is prime.

Original entry on oeis.org

349, 631, 4493, 16633, 36341

Offset: 1

Robert Price, Apr 04 2012

Harvey Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
Henri Lifchitz, Mersenne and Fermat primes field

Cf. A028491, A004061, A004062, A004063, A004023, A005808, A004064, A016054, A006032, A006033, A006034, A006035, A127995, A127996, A127997, A127998, A127999, A098438, A128002, A128003, A128004, A128005.

Select[Prime[Range[100000]], PrimeQ[(39^#-1)/38]&]

is(n)=ispseudoprime((39^n-1)/38) \\ Charles R Greathouse IV, Jun 13 2017

A185073 Numbers n such that (34^n - 1)/33 is prime.

Original entry on oeis.org

13, 1493, 5851, 6379, 125101

Offset: 1

Robert Price, Mar 10 2012

H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
H. Lifchitz, Mersenne and Fermat primes field
P. Bourdelais, A Generalized Repunit Conjecture

Cf. A028491, A004061, A004062, A004063, A004064, A004023, A005808, A016054, A006032, A006033, A006034, A006035, A098438, A127995-A128005.

Select[Prime[Range[100]], PrimeQ[(34^#-1)/33]&]

isok(n) = isprime((34^n-1)/33); \\ Michel Marcus, Mar 13 2016

lista(nn) = for(n=1, nn, if(ispseudoprime((34^n - 1)/33), print1(n, ", "))); \\ Altug Alkan, Mar 13 2016

a(5)=125101 corresponds to a probable prime discovered by Paul Bourdelais, Nov 20 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

Eric Chen, Nov 18 2014

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

			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.

Eric Chen, Table of n, a(n) for n = 1..663
Eric Chen, Table of n, a(n) for n = 1..1000 status

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).

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 *)

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

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

A294722 Numbers k such that (44^k - 1)/43 is prime.

Original entry on oeis.org

5, 31, 167, 100511

Offset: 1

Paul Bourdelais, Nov 07 2017

The number corresponding to a(4) is a probable prime.

These are the indices of base-44 repunit primes, i.e., numbers k such that A002275(k) interpreted as a base-44 number and converted to decimal is prime. - Felix Fröhlich, Nov 08 2017

P. Bourdelais, A generalized repunit conjecture

Cf. A028491, A004061, A004062, A004063, A004023, A005808, A004064, A016054, A006032, A006033, A006034, A006035, A127995, A127996, A127997, A127998, A127999, A098438, A128002, A128003, A128004, A128005, A240765.

ParallelMap[ If[ PrimeQ[(44^# - 1)/43], #, Nothing] &, Prime@Range @ 10000] (* Robert G. Wilson v, Nov 25 2017 *)

is(n) = ispseudoprime((44^n-1)/43) \\ Felix Fröhlich, Nov 08 2017

ABC2 (44^$a-1)/43 // -f{2*$a}
a: primes from 2 to 1000000

A172413 Positive numbers n such that 11^n + n + 1 is prime.

Original entry on oeis.org

1, 29, 35, 1309, 84379

Offset: 1

Matevz Markovic, Jun 30 2011

nonn

11^n + n + 1 for n = 84379 is a probable prime.

There are no further terms up to 100000.

Cf. A005808, A046867, A109076.

Do[ If[PrimeQ[11^m + m + 1 ] , Print[m]], {m, 5000}]

is(n)=ispseudoprime(11^n+n+1) \\ Charles R Greathouse IV, Jun 13 2017

cp's OEIS Frontend

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

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A141824 Antidiagonals of table A047888 (which counts longest increasing subsequences and pattern avoidances).

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A245442 Numbers n such that (50^n - 1)/49 is prime.

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A181987 Numbers n such that (39^n - 1)/38 is prime.

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A185073 Numbers n such that (34^n - 1)/33 is prime.

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

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PARI

A294722 Numbers k such that (44^k - 1)/43 is prime.

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PFGW

A172413 Positive numbers n such that 11^n + n + 1 is prime.

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