A050528 -id:A050528 - cp's OEIS frontend

A050526 Primes of form 5*2^n+1.

11, 41, 641, 40961, 163841, 167772161, 2748779069441, 180143985094819841, 188894659314785808547841, 193428131138340667952988161, 850705917302346158658436518579420528641

Offset: 1

N. J. A. Sloane, Dec 29 1999

nonn

All terms are odd since if n is even, then 5*2^n+1 is divisible by 3. - Michele Fabbrini, Jun 06 2021

Muniru A Asiru, Table of n, a(n) for n = 1..12
Ray Ballinger, Wilfried Keller, List of primes k*2^n + 1 for k < 300
Wikipedia, Proth's theorem
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

For the corresponding exponents n see A002254.

Cf. A019434, A039687, A050527, A050528, A050529, A195745, A300406, A300407, A300408.

Filtered(List([1..270], n->5*2^n + 1), IsPrime); # Muniru A Asiru, Mar 06 2018

[a: n in [1..200] | IsPrime(a) where a is 5*2^n + 1]; // Vincenzo Librandi, Mar 06 2018

a:=(n, k)->`if`(isprime(k*2^n+1), k*2^n+1, NULL):
seq(a(n, 5), n=1..127); # Martin Renner, Mar 05 2018

lista(nn) = {for(k=1, nn, if(ispseudoprime(p=5*2^k+1), print1(p, ", "))); } \\ Altug Alkan, Mar 29 2018

a(n) = A083575(A002254(n)). - Michel Marcus, Mar 29 2018

A002256 Numbers k such that 9*2^k + 1 is prime.

Original entry on oeis.org

1, 2, 3, 6, 7, 11, 14, 17, 33, 42, 43, 63, 65, 67, 81, 134, 162, 206, 211, 366, 663, 782, 1305, 1411, 1494, 2297, 2826, 3230, 3354, 3417, 3690, 4842, 5802, 6937, 7967, 9431, 13903, 22603, 24422, 39186, 43963, 47003, 49902, 67943, 114854, 127003, 145247

Offset: 1

N. J. A. Sloane

nonn

H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..60
Ray Ballinger, Proth Search Page
Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300
C. K. Caldwell, The Prime Pages
Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
R. M. Robinson, A report on primes of the form k.2^n+1 and on factors of Fermat numbers, Proc. Amer. Math. Soc., 9 (1958), 673-681.
Eric Weisstein's World of Mathematics, Proth Prime
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A050528.

Select[Range[2019],PrimeQ[9*2^#+1]&] (* Metin Sariyar, Sep 21 2019 *)

a(48) from Arkadiusz Wesolowski, Oct 22 2011
Added more terms (from http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html), Joerg Arndt, Apr 07 2013
Terms moved from Data to b-file, and more terms put in b-file, by Jeppe Stig Nielsen, Sep 21 2019

A300407 Primes of the form 17*2^n + 1.

Original entry on oeis.org

137, 557057, 2281701377, 38280596832649217, 3032901347000164747248857685080177164813336577, 240291200809860268823328460101036918152537809975084178304538443375796289537, 4031417378886400659867047414062478199819447786118941877597755244819503521544011777

Offset: 1

Martin Renner, Mar 05 2018

nonn

For the corresponding exponents n see A002259.

			From _Muniru A Asiru_, Mar 29 2018: (Start)
137 is a member because 17 * 2^3 + 1 = 137 which is a prime.
557057 is a member because 17 * 2^15 + 1 = 557057 which is a prime.
2281701377 is a member because 17 * 2^27 + 1 = 2281701377 which is a prime.
... (End)

Ray Ballinger, Wilfried Keller, List of primes k*2^n + 1 for k < 300.

Cf. A002259, A019434, A039687, A050527, A050528, A050529, A195745, A291049, A050526, A300406, A300408.

Filtered(List([1..270],n->17*2^n + 1),IsPrime); # Muniru A Asiru, Mar 06 2018

[a: n in [1..300] | IsPrime(a) where a is 17*2^n + 1]; // Vincenzo Librandi, Mar 07 2018

a:=(n,k)->`if`(isprime(k*2^n+1), k*2^n+1, NULL):
seq(a(n,17), n=1..267);

Select[Table[17 2^n + 1, {n, 400}], PrimeQ] (* Vincenzo Librandi, Mar 07 2018 *)

lista(nn) = {for(k=1, nn, if(ispseudoprime(p=17*2^k+1), print1(p, ", ")));} \\ Altug Alkan, Mar 28 2018

A300406 Primes of the form 13*2^n + 1.

Original entry on oeis.org

53, 3329, 13313, 13631489, 3489660929, 62864142619960717084721153, 5100145160001678120616578906356228963083163798627028041729, 6779255729241169695101387251026410519979286814120235842117075415451380965612384558178346467329, 1735489466685739441945955136262761093114697424414780375581971306355553527196770446893656695635969

Offset: 1

Martin Renner, Mar 05 2018

nonn

For the corresponding exponents n see A032356.

Ray Ballinger, Wilfried Keller, List of primes k*2^n + 1 for k < 300.

Cf. A019434, A039687, A032356, A050527, A050528, A050529, A173236, A195745, A050526, A300407, A300408.

Filtered(List([1..500],n->13*2^n + 1),IsPrime); # Muniru A Asiru, Mar 06 2018

[a: n in [1..400] | IsPrime(a) where a is 13*2^n + 1]; // Vincenzo Librandi, Mar 06 2018

a:=(n,k)->`if`(isprime(k*2^n+1), k*2^n+1, NULL):
seq(a(n,13), n=1..316);

Select[Table[13 2^n + 1, {n, 400}], PrimeQ] (* Vincenzo Librandi, Mar 06 2018 *)

lista(nn) = {for(k=1, nn, if(ispseudoprime(p=13*2^k+1), print1(p, ", ")));} \\ Altug Alkan, Mar 29 2018

a(n) = A168596(A032356(n)). - Michel Marcus, Mar 29 2018

A300408 Primes of the form 19*2^n + 1.

Original entry on oeis.org

1217, 19457, 1337006139375617

Offset: 1

Martin Renner, Mar 05 2018

Next term a(4) = 19*2^366 + 1 > 10^111.

For the corresponding exponents n see A032359.

Ray Ballinger, Wilfried Keller, List of primes k*2^n + 1 for k < 300.

Cf. A019434, A032359, A039687, A050527, A050528, A050529, A195745, A050526, A300406, A300407.

Filtered(List([1..500],n->19*2^n + 1),IsPrime); # Muniru A Asiru, Mar 06 2018

a:=(n,k)->`if`(isprime(k*2^n+1), k*2^n+1, NULL):
seq(a(n,19), n=1..366);

lista(nn) = {for(k=1, nn, if(ispseudoprime(p=19*2^k+1), print1(p, ", ")));} \\ Altug Alkan, Mar 29 2018

A280004 Numbers k such that 9*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m.

Original entry on oeis.org

67, 9431, 461081, 2543551

Offset: 1

Arkadiusz Wesolowski, Feb 21 2017

Fernando (Remark 5.2) shows that all terms are odd. - Jeppe Stig Nielsen, Jan 02 2025

R. Fernando, Morehead-like restrictions on Fermat divisors.
Proth Search Page, Prime factors of Fermat numbers
Eric Weisstein's World of Mathematics, Fermat Number

Subsequence of A002256.

Cf. A000215, A050528, A057778, A201364, A204620, A226366, A280003.

cp's OEIS Frontend

A050526 Primes of form 5*2^n+1.

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A002256 Numbers k such that 9*2^k + 1 is prime.

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A300407 Primes of the form 17*2^n + 1.

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A300406 Primes of the form 13*2^n + 1.

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A300408 Primes of the form 19*2^n + 1.

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A280004 Numbers k such that 9*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m.

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