A160668 Distance between prime(n) and the next higher power of 10.

8, 7, 5, 3, 89, 87, 83, 81, 77, 71, 69, 63, 59, 57, 53, 47, 41, 39, 33, 29, 27, 21, 17, 11, 3, 899, 897, 893, 891, 887, 873, 869, 863, 861, 851, 849, 843, 837, 833, 827, 821, 819, 809, 807, 803, 801, 789, 777, 773, 771, 767, 761, 759, 749, 743, 737, 731, 729, 723

Offset: 1

Author

Enoch Haga, May 23 2009

Keywords

• easy
• nonn
• base

Examples

			a(1)=8 because 10^1=10, and 10-2, 1st prime 2, = 8;
a(5)=89 because 10^2=100 and 100-11, 5th prime 11, = 89.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A055642, A061601, A160669, A160670, A228628.

Programs

Magma

[10^(Ceiling(Log(NthPrime(n))/Log(10))) - NthPrime(n): n in [1..30]]; // G. C. Greubel, May 02 2018

Maple

a:= n-> (p-> 10^length(p)-p)(ithprime(n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 08 2017

Mathematica

Table[10^Ceiling[Log[Prime[n]]/Log[10]] - Prime[n], {n, 1, 100}] (* G. C. Greubel, May 02 2018 *)

PARI

a(n) = 10^ceil(log(prime(n))/log(10)) - prime(n); \\ Michel Marcus, Dec 08 2017

UBASIC

20 N=3:print N:C=2
30 A=3:S=sqrt(N)
40 B=N/A 50 if A*B=int(N) then 70
60 A=A+2:if AEnoch Haga, May 22 2009

Formula

From Alois P. Heinz, Dec 08 2017: (Start)

a(n) = 10^A055642(A000040(n)) - A000040(n).

a(n) = A228628(n) + 1 = A061601(A000040(n)) + 1. (End)