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

%I A160668 #25 Sep 08 2022 08:45:45
%S A160668 8,7,5,3,89,87,83,81,77,71,69,63,59,57,53,47,41,39,33,29,27,21,17,11,
%T A160668 3,899,897,893,891,887,873,869,863,861,851,849,843,837,833,827,821,
%U A160668 819,809,807,803,801,789,777,773,771,767,761,759,749,743,737,731,729,723
%N A160668 Distance between prime(n) and the next higher power of 10.
%H A160668 G. C. Greubel, <a href="/A160668/b160668.txt">Table of n, a(n) for n = 1..10000</a>
%F A160668 From _Alois P. Heinz_, Dec 08 2017: (Start)
%F A160668 a(n) = 10^A055642(A000040(n)) - A000040(n).
%F A160668 a(n) = A228628(n) + 1 = A061601(A000040(n)) + 1. (End)
%e A160668 a(1)=8 because 10^1=10, and 10-2, 1st prime 2, = 8;
%e A160668 a(5)=89 because 10^2=100 and 100-11, 5th prime 11, = 89.
%p A160668 a:= n-> (p-> 10^length(p)-p)(ithprime(n)):
%p A160668 seq(a(n), n=1..100);  # _Alois P. Heinz_, Dec 08 2017
%t A160668 Table[10^Ceiling[Log[Prime[n]]/Log[10]] - Prime[n], {n, 1, 100}] (* _G. C. Greubel_, May 02 2018 *)
%o A160668 (UBASIC)
%o A160668 20 N=3:print N:C=2
%o A160668 30 A=3:S=sqrt(N)
%o A160668 40 B=N/A 50 if A*B=int(N) then 70
%o A160668 60 A=A+2:if A<S then 40
%o A160668 70 if N=prmdiv(N) then print N;:else 130
%o A160668 80 if alen(N)=1 then print 10^1-N;:P=prmdiv(10^1-N):goto 120
%o A160668 90 if alen(N)=2 then print 10^2-N;:P=prmdiv(10^2-N):goto 120
%o A160668 100 if alen(N)=3 then print 10^3-N;:P=prmdiv(10^3-N):goto 120
%o A160668 110 if alen(N)=4 then print 10^4-N;:P=prmdiv(10^4-N)
%o A160668 120 print P;C:C=C+1:stop
%o A160668 130 N=N+2:S=sqrt(N):goto 40
%o A160668 140 'recipseq, _Enoch Haga_, May 22 2009
%o A160668 (PARI) a(n) = 10^ceil(log(prime(n))/log(10)) - prime(n); \\ _Michel Marcus_, Dec 08 2017
%o A160668 (Magma) [10^(Ceiling(Log(NthPrime(n))/Log(10))) - NthPrime(n): n in [1..30]]; // _G. C. Greubel_, May 02 2018
%Y A160668 Cf. A000040, A055642, A061601, A160669, A160670, A228628.
%K A160668 easy,nonn,base
%O A160668 1,1
%A A160668 _Enoch Haga_, May 23 2009