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

Author

Vasiliy Danilov (danilovv(AT)usa.net)

Keywords

• nonn

Examples

			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.
		

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.

Crossrefs

Cf. A003617, A013632, A033874, A097517.

Programs

Magma

[NextPrime(10^n)-10^n: n in [0..65]]; // Vincenzo Librandi, Sep 13 2016

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 *)

PARI

a(n)=nextprime(10^n)-10^n \\ Charles R Greathouse IV, Jul 16 2011

Formula

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

Extensions

More terms from Patrick De Geest