A033874 Difference between the largest prime < 10^n (A003618) and 10^n.

3, 3, 3, 27, 9, 17, 9, 11, 63, 33, 23, 11, 29, 27, 11, 63, 3, 11, 39, 11, 101, 27, 23, 257, 123, 141, 99, 209, 27, 11, 27, 21, 9, 411, 23, 159, 81, 59, 57, 17, 119, 83, 81, 53, 9, 33, 41, 33, 57, 57, 323, 231, 177, 291, 111, 593, 93, 149, 141, 161, 39, 83, 123, 51, 269

Offset: 1

Author

Vasiliy Danilov (danilovv(AT)usa.net)

Keywords

• nonn
• nice

Examples

			a(4) = 27 because 10^4 - 9973 = 27. The 21st term is 101 since 10^21 - 101 = 999999999999999999899 is prime.
		

References

• Knuth, Art of Computer Programming, volume 2, pages 13 and 390.
• Journal of Recreational Mathematics, volume 14, number 4, page 285.
• Journal of Recreational Mathematics, volume 20 ,number 3, page 209-210.
• O'Hara, J. Rec. Math., 22 (1990), Table on page 278.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..8000 (first 1000 terms from T. D. Noe)
• V. Danilov, Table for large n
• Eric Weisstein's World of Mathematics, Previous 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. A003618, A033873.

Programs

Magma

[10^n-PreviousPrime(10^n): n in [1..65]]; // Vincenzo Librandi, Sep 13 2016

Maple

seq(10^n-prevprime(10^n),n=1..65); # Emeric Deutsch, Apr 20 2006

Mathematica

PrevPrime[ n_Integer ] := Module[ {k}, k = n - 1; While[ ! PrimeQ[ k ], k-- ]; k ]; Table[ 10^n - PrevPrime[ 10^n ], {n, 1, 75} ] (* Robert G. Wilson v, Sep 09 2000 *)
Table[10^i - NextPrime[10^i, -1], {i, 0, 70}] (* Harvey P. Dale, Jan 13 2011 *)

PARI

a(n)=10^n-precprime(10^n) \\ Charles R Greathouse IV, Aug 03 2014

Extensions

More terms from Patrick De Geest