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 1-6 of 6 results.

A160027 Primes of the form 2^(2^k)+15.

Original entry on oeis.org

17, 19, 31, 271, 65551, 4294967311
Offset: 1

Views

Author

Cino Hilliard, Apr 30 2009

Keywords

Comments

Fermat primes of order 15.
The number of Fermat primes of order 15 exceeds the number of known Fermat primes.
Terms given correspond to n= 0, 1, 2, 3, 4 and 5.
Next term >= 2^2^16 + 15. - Vincenzo Librandi, Jun 07 2016
Next term >= 2^2^17 + 15. - Charles R Greathouse IV, Jun 07 2016

Examples

			For k = 5, 2^32 + 15 = 4294967311 is prime.

Crossrefs

Cf. A019434 (order 1), A104067 (superset for order 13), A160028 (order 81).
Cf. similar sequences listed in A273547.

Programs

  • Magma
    [a: n in [0..15] | IsPrime(a) where a is 2^(2^n)+15]; // Vincenzo Librandi, Jun 07 2016
  • Mathematica
    Select[Table[2^(2^n) + 15, {n, 0, 10}], PrimeQ] (* Vincenzo Librandi, Jun 07 2016 *)
  • PARI
    g(n,m) = for(x=0,n,y=2^(2^x)+m;if(ispseudoprime(y),print1(y",")))

Formula

Intersection of the primes and the set of Fermat numbers F(k,m) = 2^(2^k)+m of order m=15.

Extensions

Edited by R. J. Mathar, May 08 2009

A253772 Numbers k such that 4^k + 13 is prime.

Original entry on oeis.org

1, 2, 4, 10, 19, 32, 40, 146, 566, 2054, 9967, 62639, 87814, 141092
Offset: 1

Views

Author

Vincenzo Librandi, Jan 12 2015

Keywords

Comments

Numbers of the form 4^n+k (for n>0) are never primes when k is even (obviously) or when k == -1 (mod 6): in the last case, in fact, (3+1)^n + 6*h-1 is divisible by 3. - Bruno Berselli, Oct 06 2015

Crossrefs

Cf. A104067.
Cf. Numbers k such that 4^k + d is prime: A089437 (d=3), A217349 (d=7), A217350 (d=9), this sequence (d=13), A253773 (d=15), A253774 (d=19), A262345 (d=21), A204388 (d=25), A262969 (d=27), A262971 (d=31), A262972 (d=33).

Programs

  • Magma
    [n: n in [0..2000] | IsPrime(4^n+13)];
  • Mathematica
    Select[Range[4000], PrimeQ[4^# + 13] &]
  • PARI
    is(n)=ispseudoprime(4^n+13) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = A102634(n)/2. - Elmo R. Oliveira, Nov 12 2023

Extensions

a(11)-a(14) derived from A102634 by Robert Price, Sep 06 2015

A243429 Primes of the form 2^n + 39.

Original entry on oeis.org

41, 43, 47, 71, 103, 167, 1063, 2087, 8231, 131111, 536870951, 8589934631, 549755813927, 8796093022247, 154742504910672534362390567, 40564819207303340847894502572071, 162259276829213363391578010288167, 2722258935367507707706996859454145691687
Offset: 1

Views

Author

Vincenzo Librandi, Jun 05 2014

Keywords

Comments

Associated n: 1, 2, 3, 5, 6, 7, 10, 11, 13, 17, 29, 33, 39, 43, 87, 105, 107, 131, 253, 329, ....

Links

Crossrefs

Cf. primes of the form 2^n+k: A092506 (k=1), A057733 (k=3), A123250 (k=5), A104066 (k=7), A104070 (k=9), A156940 (k=11), A104067 (k=13), A144487 (k=15), A156973 (k=17), A104068 (k=19), A156983 (k=21), A176922 (k=23), A104072 (k=25), A104071 (k=27), A156974 (k=29), A104069 (k=31), A176926 (k=33), A176927 (k=35), A176924 (k=37), this sequence (k=39), A176925 (k=41), A243430 (k=43), A243431 (k=45), A243432 (k=47), A104073 (k=49).

Programs

  • Magma
    [a: n in [0..500] | IsPrime(a) where a is 2^n+39];
  • Mathematica
    Select[Table[2^n + 39, {n, 0, 500}], PrimeQ]

A156973 Primes of the form 2^k + 17.

Original entry on oeis.org

19, 8209, 2097169, 8589934609, 2417851639229258349412369, 680564733841876926926749214863536422929, 62165404551223330269422781018352605012557018849668464680057997111644937126566671941649
Offset: 1

Views

Author

Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 19 2009

Keywords

Examples

			19 = 2^1 + 17 is in the sequence;
8209 = 2^13 + 17 is in the sequence.

Crossrefs

Cf. A000040, A057200, A057733 (2^k + 3), A123250 (2^k + 5), A104066 (2^k + 7), A156940 (2^k + 11), A104067 (2^k + 13).

Programs

  • Magma
    [ a: n in [1..400] | IsPrime(a) where a is 2^n+17 ]; // Vincenzo Librandi, Nov 27 2010
  • Mathematica
    Delete[Union[Table[If[PrimeQ[2^n + 17], 2^n + 17, 0], {n, 1, 300}]],1]

Formula

a(n) = 2^A057200(n) + 17. - Elmo R. Oliveira, Nov 08 2023

Extensions

a(7) from Vincenzo Librandi, Apr 29 2010

A172183 a(n) is the smallest prime of the form p^q+n, where p and q are prime, or zero if no such prime exists.

Original entry on oeis.org

5, 11, 7, 13, 13, 31, 11, 17, 13, 19, 19, 37, 17, 23, 19, 41, 8209, 43, 23, 29, 29, 31, 31, 73, 29, 53, 31, 37, 37, 79, 0, 41, 37, 43, 43, 61, 41, 47, 43, 67, 73, 67, 47, 53, 53, 71, 79, 73, 53, 59, 59, 61, 61, 79, 59, 83, 61, 67, 67, 109, 0, 71, 67, 73, 73, 191, 71, 193, 73, 79
Offset: 1

Views

Author

Cheng Zhang (cz1(AT)rice.edu), Jan 28 2010, Mar 02 2010

Keywords

Comments

If n mod 6 = 1, both p and q must be 2, and a(n)=0 if n + 4 is not a prime. The values of a(n) for n=257,297,353,383,557 are either greater than 176 000 or 0. Several large entries: a(87) = 2^25633 + 87, a(717) = 2^3217 + 717, a(773) = 2^2539 + 773, a(927) = 2^1117 + 927.

Examples

			a(1)=5 because 5=2^2+1 is the smallest prime of the form p^q+1. a(2)=11 because 11=3^2+2. a(3)=7, because 7=2^2+3. a(17)=8209, because 8209=2^13+17. a(31)=0, because p^q+31 cannot be a prime.

Crossrefs

Cf. A123318, A056208, A056206, A057733, A123250, A104066, A156940, A104067, A156973

Programs

  • Mathematica
    For[l = {}; n = 1, n <= 70, n++, found = False; If[Mod[n, 2] == 0, For[rm = Infinity; i = 1, i < 100, i++, For[j = 1, j < 100, j++, p = Prime[i]; q = Prime[j]; r = p^q + n; If[r >= rm, Break[], If[PrimeQ[r], rm = r; found = True]]; ]; ], (* if n is odd, r=2^q+n *) If[Mod[n, 6] == 1, r = 4 + n; If[PrimeQ[r], found = True], For[j = 1, j < 1000, j++, q = Prime[j]; r = 2^q + n; If[PrimeQ[r], found = True; rm = r; Break[]]; ]; ]; ]; If[ ! found, rm = 0]; l = Append[l, rm]; ]; l

A274023 Primes of the form 2^(2^k) + 13.

Original entry on oeis.org

17, 29, 269, 18446744073709551629
Offset: 1

Views

Author

Vincenzo Librandi, Jun 07 2016

Keywords

Comments

Terms given correspond to k = 1, 2, 3 and 6.
Next term >= 2^2^39 + 13. - Charles R Greathouse IV, Jun 08 2016

Crossrefs

Cf. A019434, A104067, A130730, A274022.
Cf. similar sequences listed in A273547.

Programs

  • Magma
    [a: n in [0..10] | IsPrime(a) where a is 2^(2^n)+13];
  • Mathematica
    Select[Table[2^(2^n) + 13, {n, 0, 15}], PrimeQ]
  • PARI
    for(n=1,6, if(ispseudoprime(t=2^2^n+13), print1(t", "))) \\ Charles R Greathouse IV, Jun 08 2016
Showing 1-6 of 6 results.

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