A054321 -id:A054321 - cp's OEIS frontend

A014210 Next prime after 2^n.

2, 3, 5, 11, 17, 37, 67, 131, 257, 521, 1031, 2053, 4099, 8209, 16411, 32771, 65537, 131101, 262147, 524309, 1048583, 2097169, 4194319, 8388617, 16777259, 33554467, 67108879, 134217757, 268435459, 536870923, 1073741827, 2147483659

Offset: 0

N. J. A. Sloane

nonn

Except for a(1) = 3 instead of 2, a(n) is the least prime obtained as a binomial transform of n numbers. E.g. a(5) = (1,5,10,10,5,1).(1,1,1,1,1,6)= 37. - Amarnath Murthy, Nov 26 2003
a(n) is the smallest m for which m>(tau(m))^n, where tau(m) is the number of divisors of m. [Vladimir Shevelev, May 31 2010]
Equivalently, "Smallest prime > 2^n" while in A104080 it is "Smallest prime >= 2^n". The only difference is the 2nd term with a(1) = 3 and A104080(1) = 2. - Bernard Schott, Oct 30 2020

J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 615 pp. 82 and 279, Ellipses, Paris, 2004. Warning : gives Sum_{k>=1} 1/A104080(k) = 0.7404...

Jens Kruse Andersen, Table of n, a(n) for n = 0..1000

See A203074 for another version.

Cf. A014211, A014234, A054321, A104080, A338475.

Maple
```
[ seq( nextprime( 2^i ),i=0..40) ];
```

NextPrime[ n_Integer] := (k = n + 1; While[ !PrimeQ[k], k++ ]; k); Table[ NextPrime[2^n], {n, 0, 35} ]
f[n_] := NextPrime[2^n]; Array[f, 30, 0] (* Robert G. Wilson v, Jun 05 2015 *)
NextPrime[2^Range[0,40]] (* Harvey P. Dale, Jun 22 2017 *)

a(n) = nextprime(2^n+1); \\ Michel Marcus, Oct 30 2020

Sum_{k>=0} 1/a(k) = A338475. - Bernard Schott, Oct 30 2020

A013599 a(n) = nextprime(5^n) - 5^n.

Original entry on oeis.org

1, 2, 4, 2, 6, 12, 4, 12, 22, 26, 4, 14, 58, 6, 12, 42, 24, 2, 12, 56, 48, 24, 18, 38, 58, 14, 12, 38, 34, 62, 28, 92, 214, 122, 102, 168, 136, 18, 48, 102, 108, 126, 18, 126, 76, 108, 22, 204, 52, 122, 96, 114, 94, 14, 52, 38, 58, 248, 64, 56, 16, 102, 106

Offset: 0

James Kilfiger (mapdn(AT)csv.warwick.ac.uk)

nonn

Zak Seidov, Table of n, a(n) for n = 0..500

Cf. A000351, A013632, A054321, A151800,

Maple
```
seq(nextprime(5^i)-5^i, i=0..100);
```

NextPrime[#]-#&/@(5^Range[0,70]) (* Harvey P. Dale, Sep 29 2011 *)

a(n) = nextprime(5^n+1) - 5^n; \\ Michel Marcus, Jun 14 2020

a(n) = A151800(5^n)-5^n = A054321(n)-5^n = A013632(5^n). - R. J. Mathar, Nov 28 2016

A104090 Largest prime <= 5^n.

Original entry on oeis.org

5, 23, 113, 619, 3121, 15619, 78121, 390581, 1953109, 9765619, 48828113, 244140613, 1220703073, 6103515623, 30517578121, 152587890563, 762939453109, 3814697265523, 19073486328109, 95367431640599, 476837158203071, 2384185791015571, 11920928955078089

Offset: 1

Cino Hilliard, Mar 03 2005

Cf. A014234, A054321, A104088, A104089, A104091-A104094, A003618, A104096.

Cf. A000040, A000351, A007917.

NextPrime[5^Range[30] + 1, -1] (* Paolo Xausa, Oct 29 2024 *)

g(n,b) = for(x=0,n,print1(precprime(b^x)","))

a(n) = A007917(A000351(n)). - Paolo Xausa, Oct 29 2024

A104083 Smallest prime >= 5^n.

Original entry on oeis.org

2, 5, 29, 127, 631, 3137, 15629, 78137, 390647, 1953151, 9765629, 48828139, 244140683, 1220703131, 6103515637, 30517578167, 152587890649, 762939453127, 3814697265637, 19073486328181, 95367431640673, 476837158203149

Offset: 0

Cino Hilliard, Mar 03 2005

Join[{2,5},NextPrime[5^Range[2,30]]] (* Harvey P. Dale, Feb 23 2016 *)

g(n,b) = for(x=0,n,print1(nextprime(b^x)","))

a(n)=A054321(n), n>1. [From R. J. Mathar, Dec 13 2008]

cp's OEIS Frontend

A014210 Next prime after 2^n.

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A013599 a(n) = nextprime(5^n) - 5^n.

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A104090 Largest prime <= 5^n.

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A104083 Smallest prime >= 5^n.

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