login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014210 Next prime after 2^n. 31
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

REFERENCES

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...

LINKS

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

FORMULA

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

MAPLE

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

MATHEMATICA

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 *)

PROG

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

CROSSREFS

See A203074 for another version.

Cf. A014211, A054321, A104080, A338475.

Sequence in context: A175247 A298598 A079370 * A203074 A014556 A062737

Adjacent sequences:  A014207 A014208 A014209 * A014211 A014212 A014213

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 20:51 EST 2020. Contains 338965 sequences. (Running on oeis4.)