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The non-powers of 10.
3

%I #12 Oct 11 2024 13:19:59

%S 0,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,

%T 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,

%U 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70

%N The non-powers of 10.

%C a(n) is the length signature of a string plus its length.

%F a(n) = ceiling(log_10(a(n) + 1)) + n.

%F Find k such that 10^k - (k + 1) <= n < 10^(k+1) - (k + 2), then a(n) = n + k + 1.

%t With[{upto=100},Complement[Range[0,upto],10^Range[0,Floor[Log10[ upto]]]]] (* _Harvey P. Dale_, Nov 01 2016 *)

%o (Python)

%o def A057717(n): return n+(m:=len(str(n-1)))+(n>=10**m-m) if n else 0 # _Chai Wah Wu_, Jun 30 2024

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o yield 0

%o yield from (j for i in count(0) for j in range(10**i+1, 10**(i+1)))

%o print(list(islice(agen(), 70))) # _Michael S. Branicky_, Oct 11 2024

%Y Complement of A011557. Cf. A057716.

%K nonn

%O 0,2

%A John Lindgren (john.lindgren(AT)Eng.Sun.COM), Oct 24 2000

%E Better description from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 29 2001