A206286 Nonprime numbers starting with a digit 1.

1, 10, 12, 14, 15, 16, 18, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 152, 153, 154, 155, 156, 158

Offset: 1

Author

Jaroslav Krizek, Feb 12 2012

Keywords

• nonn
• base

Comments

Complement of A045707 with respect to A131835. Supersequence of A206288.

Crossrefs

Cf. A045707 (primes with first digit 1), A131835 (numbers starting with a digit 1).

Cf. A206288.

Programs

Mathematica

Select[Range[200], ! PrimeQ[#] && IntegerDigits[#][[1]] == 1 &] (* T. D. Noe, Feb 13 2012 *)

Python

from sympy import primepi
def A206286(n):
    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))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Dec 10 2024