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

1,1

Links

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

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)

Example

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.

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 *)

Prog

(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 A<S then 40
70 if N=prmdiv(N) then print N; :else 130
80 if alen(N)=1 then print 10^1-N; :P=prmdiv(10^1-N):goto 120
90 if alen(N)=2 then print 10^2-N; :P=prmdiv(10^2-N):goto 120
100 if alen(N)=3 then print 10^3-N; :P=prmdiv(10^3-N):goto 120
110 if alen(N)=4 then print 10^4-N; :P=prmdiv(10^4-N)
120 print P; C:C=C+1:stop
130 N=N+2:S=sqrt(N):goto 40
140 'recipseq, Enoch Haga, May 22 2009
(PARI) a(n) = 10^ceil(log(prime(n))/log(10)) - prime(n); \\ Michel Marcus, Dec 08 2017
(Magma) [10^(Ceiling(Log(NthPrime(n))/Log(10))) - NthPrime(n): n in [1..30]]; // G. C. Greubel, May 02 2018

Crossrefs

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

Sequence in context: A316728 A231098 A072003 * A086033 A246504 A182527

Adjacent sequences: A160665 A160666 A160667 * A160669 A160670 A160671

Keyword

easy,nonn,base

Author

Enoch Haga, May 23 2009

Status

approved