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Distance between prime(n) and the next higher power of 10.
4

%I #25 Sep 08 2022 08:45:45

%S 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 3,899,897,893,891,887,873,869,863,861,851,849,843,837,833,827,821,

%U 819,809,807,803,801,789,777,773,771,767,761,759,749,743,737,731,729,723

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

%H G. C. Greubel, <a href="/A160668/b160668.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Alois P. Heinz_, Dec 08 2017: (Start)

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

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

%e a(1)=8 because 10^1=10, and 10-2, 1st prime 2, = 8;

%e a(5)=89 because 10^2=100 and 100-11, 5th prime 11, = 89.

%p a:= n-> (p-> 10^length(p)-p)(ithprime(n)):

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Dec 08 2017

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

%o (UBASIC)

%o 20 N=3:print N:C=2

%o 30 A=3:S=sqrt(N)

%o 40 B=N/A 50 if A*B=int(N) then 70

%o 60 A=A+2:if A<S then 40

%o 70 if N=prmdiv(N) then print N;:else 130

%o 80 if alen(N)=1 then print 10^1-N;:P=prmdiv(10^1-N):goto 120

%o 90 if alen(N)=2 then print 10^2-N;:P=prmdiv(10^2-N):goto 120

%o 100 if alen(N)=3 then print 10^3-N;:P=prmdiv(10^3-N):goto 120

%o 110 if alen(N)=4 then print 10^4-N;:P=prmdiv(10^4-N)

%o 120 print P;C:C=C+1:stop

%o 130 N=N+2:S=sqrt(N):goto 40

%o 140 'recipseq, _Enoch Haga_, May 22 2009

%o (PARI) a(n) = 10^ceil(log(prime(n))/log(10)) - prime(n); \\ _Michel Marcus_, Dec 08 2017

%o (Magma) [10^(Ceiling(Log(NthPrime(n))/Log(10))) - NthPrime(n): n in [1..30]]; // _G. C. Greubel_, May 02 2018

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

%K easy,nonn,base

%O 1,1

%A _Enoch Haga_, May 23 2009