A033873 Difference between first prime > 10^n (A003617) and 10^n.

1, 1, 1, 9, 7, 3, 3, 19, 7, 7, 19, 3, 39, 37, 31, 37, 61, 3, 3, 51, 39, 117, 9, 117, 7, 13, 67, 103, 331, 319, 57, 33, 49, 61, 193, 69, 67, 43, 133, 3, 121, 109, 63, 57, 31, 9, 121, 33, 193, 9, 151, 121, 327, 171, 31, 21, 3, 279, 159, 19, 7, 93, 447, 121, 57, 49, 49, 49, 99, 9

Offset

0,4

References

O'Hara, J. Rec. Math., 22 (1990), Table on page 278.

Links

Matthias Baur, Table of n, a(n) for n = 0..14000 (terms 0..1000 from T. D. Noe, terms 1001..2750 from Robert G. Wilson v, terms 2751..8000 from Giovanni Resta)

Eric Weisstein's World of Mathematics, Next Prime

R. G. Wilson, v., Extract from letter to N. J. A. Sloane, May 20 1994, with annotated scanned copy of page 278 of O'Hara article.

Formula

a(n) = A003617(n) - 10^n = A013632(10^n). - Robert Israel, Aug 10 2015

Example

The 23rd term is 117 since 10^23 + 117 = 100000000000000000000117 is prime and all of 100000000.., 100000....001, 1000...002 up through 1000...000116 are composite.

Maple

seq(nextprime(10^n)-10^n, n=0..70); # Emeric Deutsch, Apr 20 2006

Mathematica

f[n_]:=Module[{x=10^n}, NextPrime[x]-x]; f/@Range[0, 75]  (* Harvey P. Dale, Mar 30 2011 *)

Prog

(PARI) a(n)=nextprime(10^n)-10^n \\ Charles R Greathouse IV, Jul 16 2011
(Magma) [NextPrime(10^n)-10^n: n in [0..65]]; // Vincenzo Librandi, Sep 13 2016

Crossrefs

Cf. A003617, A013632, A033874, A097517.

Sequence in context: A002205 A363766 A251734 * A260880 A135449 A060388

Adjacent sequences: A033870 A033871 A033872 * A033874 A033875 A033876

Keyword

nonn

Author

Vasiliy Danilov (danilovv(AT)usa.net)

Extensions

More terms from Patrick De Geest

Status

approved