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%I #14 Dec 10 2024 09:57:36
%S 1,10,12,14,15,16,18,100,102,104,105,106,108,110,111,112,114,115,116,
%T 117,118,119,120,121,122,123,124,125,126,128,129,130,132,133,134,135,
%U 136,138,140,141,142,143,144,145,146,147,148,150,152,153,154,155,156,158
%N Nonprime numbers starting with a digit 1.
%C Complement of A045707 with respect to A131835. Supersequence of A206288.
%t Select[Range[200], ! PrimeQ[#] && IntegerDigits[#][[1]] == 1 &] (* _T. D. Noe_, Feb 13 2012 *)
%o (Python)
%o from sympy import primepi
%o def A206286(n):
%o def f(x): return n-1+x+((m:=10**(l:=len(str(x))-1))-(k:=min((m<<1)-1,x))-primepi(m-1)+primepi(k))-sum((m:=10**i)+primepi(m-1)-primepi((m<<1)-1) for i in range(l))
%o m, k = n, f(n)
%o while m != k: m, k = k, f(k)
%o return m # _Chai Wah Wu_, Dec 10 2024
%Y Cf. A045707 (primes with first digit 1), A131835 (numbers starting with a digit 1).
%Y Cf. A206288.
%K nonn,base
%O 1,2
%A _Jaroslav Krizek_, Feb 12 2012