A253772 -id:A253772 - cp's OEIS frontend

A102634 Numbers k such that 2^k + 13 is prime.

2, 4, 8, 20, 38, 64, 80, 292, 1132, 4108, 19934, 125278, 175628, 282184

Offset: 1

Lei Zhou, Jan 20 2005

If k is odd, then 2^k + 13 is divisible by 3. - Robert G. Wilson v, Jan 24 2005
a(15) > 5*10^5. - Robert Price, Aug 15 2015
For k in this sequence, the number 2^(k-1)*(2^k+13) has deficiency 14, cf. A141550. - M. F. Hasler, Jul 18 2016

			2^2+13 = 17 is prime.
2^4+13 = 29 is prime.
2^3+13 = 21 is not prime.

H. Lifchitz and R. Lifchitz (Editors), PRP Top Records, of the form 2^n+13.
Lei Zhou, Between 2^n and primes [broken link].

Cf. A019434 (2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), A057196 (2^k+9), A102633 (2^k+11), A102634 (this), A057197 (2^k+15), A057200 (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23).

Do[m = n; If[PrimeQ[2^n + 13], Print[n]], {n, 2, 19125, 2}] (* Robert G. Wilson v, Jan 24 2005 *)

first(m)=my(v=vector(m),r=1);for(i=1,m,while(!isprime(2^r + 13),r++);v[i]=r;r++);v; \\ Anders Hellström, Aug 15 2015

a(n) = 2*A253772(n). - Elmo R. Oliveira, Nov 12 2023

a(10) from Robert G. Wilson v, Jan 24 2005

a(11)-a(14) from Robert Price, Aug 15 2015

A261539 Numbers m such that (4^m + 5) / 3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 12, 21, 42, 150, 195, 390, 411, 1215, 2754, 2757, 3246, 6186, 11340, 12885, 84708, 87120, 191772, 503919, 786441

Offset: 1

Vincenzo Librandi, Aug 25 2015

After 1, m is not of the form 3*k+1 because in this case 4^m+5 is divisible by 9; after 2, m is not of the form 3*k+2 because in this case 4^m+5 is divisible by 7. Therefore, m>2 is always a multiple of 3. - Bruno Berselli, Aug 25 2015

Larger members of the sequence generate probable primes only. - Serge Batalov, Aug 27 2015

			6 is in the sequence because (4^6+5)/3 = 1367 is prime.
9 is in the sequence because (4^9+5)/3 = 87383 is prime.
4 is not in the sequence because (4^4+5)/3 = 87 = 3*29 is not prime.

Henri & Renaud Lifchitz PRPtop, (2^n+5)/3 PRPs

Cf. A163834.
Cf. numbers n such that (4^n+k)/3 is prime: this sequence (k=5), A261577 (k=11), A261578 (k=17), A261579 (k=23).
Cf. A253772.

[n: n in [0..1000] | IsPrime((4^n+5) div 3)];

Select[Range[0, 5000], PrimeQ[(4^# + 5)/3] &]

isok(n)=isprime((4^n + 5) / 3) \\ Anders Hellström, Aug 25 2015

a(18)-a(23) from Lelio R Paula (2012-2014) via Serge Batalov, Aug 27 2015

a(24)-a(25) from Serge Batalov, Aug 29 2015

A253773 Numbers k such that 4^k + 15 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 11, 13, 15, 16, 20, 21, 23, 36, 38, 90, 99, 155, 164, 171, 254, 255, 273, 404, 1386, 1941, 1970, 2420, 3759, 5559, 5776, 6369, 6429, 22061, 32330, 81780, 90248, 162933, 240920, 504584

Offset: 1

Vincenzo Librandi, Jan 12 2015

Half of even terms of A057197. - Michel Marcus, Aug 28 2015

			For k = 15, 4^15 + 15 = 1073741839 is prime.

Cf. A057197, A237418, A253772 (similar sequence).

Magma
```
[n: n in [0..1300] | IsPrime(4^n+15)];
```

Select[Range[10000], PrimeQ[4^# + 15] &]

is(n)=isprime(4^n + 15) \\ Anders Hellström, Aug 28 2015

a(31)-a(39) from A057197 data by Michel Marcus, Aug 28 2015
a(40) derived from A057197 by Robert Price, Sep 18 2015
a(41) from A057197 data by Elmo R. Oliveira, Dec 11 2023

A253774 Numbers k such that 4^k + 19 is prime.

Original entry on oeis.org

1, 3, 15, 81, 327, 357, 685, 831, 861, 1405, 38571, 78127, 216487, 546121, 622615

Offset: 1

Vincenzo Librandi, Jan 16 2015

			15 is a term because 4^15 + 19 = 1073741843 is prime.

Cf. A057221, A104068, A253772 (similar sequence).

Magma
```
[n: n in [0..700] | IsPrime(4^n+19)];
```
Mathematica
```
Select[Range[3000], PrimeQ[4^# + 19] &]
```

is(n)=ispseudoprime(4^n+19) \\ Charles R Greathouse IV, Jun 06 2017

a(n) = A057221(n)/2. - Joerg Arndt, Aug 28 2015

Three more term (using A057221) from Joerg Arndt, Aug 28 2015

a(14)-a(15) derived from A057221 by Elmo R. Oliveira, Nov 28 2023

A262971 Numbers k such that 4^k + 31 is prime.

Original entry on oeis.org

2, 6, 18, 270, 422, 596, 6068, 42140, 64178, 158732, 1509278

Offset: 1

Robert Price, Oct 05 2015

The next terms are > 1.5*10^6.

Contains exactly the halved even terms of A247952.

			For k = 18, 4^18 + 31 = 68719476767 is prime.

Cf. A247952, A253772 (similar sequence).

[n: n in [0..700] | IsPrime(4^n+31)]; // Vincenzo Librandi, Oct 06 2015

Select[Range[0, 250000], PrimeQ[4^# + 31] &]

for(n=1, 1e3, if(isprime(4^n+31), print1(n", "))) \\ Altug Alkan, Oct 06 2015

a(n) = A247952(n)/2. - Elmo R. Oliveira, Nov 28 2023

a(11) derived from A247952 by Elmo R. Oliveira, Nov 28 2023

A262345 Numbers k such that 4^k + 21 is prime.

Original entry on oeis.org

2, 4, 8, 22, 24, 26, 98, 228, 246, 808, 1556, 1792, 1978, 3424, 69738, 108376, 169584

Offset: 1

Robert Price, Sep 18 2015

Half of even terms of A057201. - Elmo R. Oliveira, Nov 29 2023

			For k = 26, 4^26 + 21 = 4503599627370517 is prime.

Cf. A057201, A156983, A253772.

Magma
```
[n: n in [0..700] | IsPrime(4^n+21)];
```
Mathematica
```
Select[Range[3000], PrimeQ[4^# + 21] &]
```

for(n=1, 1e3, if(isprime(4^n+21), print1(n", "))) \\ Altug Alkan, Sep 18 2015

A262969 Numbers k such that 4^k + 27 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 20, 22, 43, 55, 67, 77, 92, 97, 154, 160, 533, 748, 1432, 3143, 6427, 8257, 8270, 9623, 12269, 28822, 32683, 42638, 97427, 133340, 188395, 239044

Offset: 1

Robert Price, Oct 05 2015

The next terms are > 239044.

Contains exactly the halved even terms of A157007.

			For k = 22, 4^22 + 27 = 17592186044443 is prime.

Cf. A157007, A253772 (similar sequence).

[n: n in [0..700] | IsPrime(4^n+27)]; // Vincenzo Librandi, Oct 06 2015

Select[Range[0, 250000], PrimeQ[4^# + 27] &]

for(n=1, 1e3, if(isprime(4^n+3^3), print1(n", "))) \\ Altug Alkan, Oct 06 2015

a(32) derived from A157007 by Elmo R. Oliveira, Nov 28 2023

A262972 Numbers k such that 4^k + 33 is prime.

Original entry on oeis.org

1, 3, 6, 7, 10, 15, 30, 34, 54, 58, 103, 105, 205, 223, 279, 741, 2098, 3523, 9210, 37674, 89895, 101509, 217123

Offset: 1

Robert Price, Oct 05 2015

Contains exactly the halved even terms of A247953.

The next terms are > 2*10^5.

			For k = 30, 4^30 + 33 = 1152921504606847009 is prime.

Cf. A247953, A253772 (similar sequence).

[n: n in [0..700] | IsPrime(4^n+33)]; // Vincenzo Librandi, Oct 06 2015

Select[Range[0, 250000], PrimeQ[4^# + 33] &]

for(n=1, 1e3, if(isprime(4^n+33), print1(n", "))) \\ Altug Alkan, Oct 06 2015

a(23) derived from A247953 by Elmo R. Oliveira, Nov 28 2023

cp's OEIS Frontend

A102634 Numbers k such that 2^k + 13 is prime.

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A261539 Numbers m such that (4^m + 5) / 3 is prime.

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A253773 Numbers k such that 4^k + 15 is prime.

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A253774 Numbers k such that 4^k + 19 is prime.

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A262971 Numbers k such that 4^k + 31 is prime.

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Magma

Mathematica

PARI

Formula

Extensions

A262345 Numbers k such that 4^k + 21 is prime.

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Examples

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Programs

Magma

Mathematica

PARI

A262969 Numbers k such that 4^k + 27 is prime.

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Author

Keywords

Comments