A157709 -id:A157709 - cp's OEIS frontend

A157712 Smallest prime made up of 0's and prime(n) 1's (or 0 when no such prime exists).

11, 0, 101111, 11110111, 101111111111, 101101111111111, 101111111111111111, 1111111111111111111, 11111111111111111111111, 111110111111111111111111111111, 11111101111111111111111111111111

Offset: 1

Lekraj Beedassy, Mar 04 2009

Smallest prime with digit sum A000040(n) and using only 0's and 1's. Subsequence of A157709.

Chai Wah Wu, Table of n, a(n) for n = 1..168

Cf. A054750.

from _future_ import division
from itertools import combinations
from sympy import prime, isprime
def A157712(n):
    if n == 1:
        return 11
    if n == 2:
        return 0
    p = prime(n)
    l = p
    while True:
        for i in combinations(range(l),l-p):
            s = ['1']*l
            for x in i:
                s[x] = '0'
            q = int(''.join(s))
            if isprime(q):
                return q
        l += 1 # Chai Wah Wu, Nov 05 2015

Extended by Ray Chandler, Mar 06 2009

A261173 Table read by antidiagonals: T(n,k) = smallest prime p containing only digits 0 and 1 with n 0's and k 1's, or 0 if no such p exists.

Original entry on oeis.org

11, 0, 101, 0, 0, 0, 0, 10111, 0, 0, 0, 101111, 0, 0, 0, 0, 0, 0, 1011001, 0, 0, 0, 11110111, 0, 10011101, 10010101, 0, 0, 0, 101111111, 101101111, 0, 100100111, 101001001, 0, 0, 0, 0, 1010111111, 1001110111, 0, 1000011011, 1000001011, 0, 0

Offset: 0

Felix Fröhlich, Aug 10 2015

T(n, k) = 0 if k is a term of A008585.
T(0, k) != 0 iff k is a term of A004023.
T(1, k) = A157709(k-2) for all k >= 4.
T(n, 2) != 0 iff A062397(n+1) is prime.
a(n) is in A168586 iff it is the smallest p in T with A007953(p) = k.

			Table T(n, k) starts
     k = 2        3        4        5
      -------------------------------------
n = 0 |  11       0        0        0
n = 1 |  101      0        10111    101111
n = 2 |  0        0        0        0
n = 3 |  0        0        1011001  10011101

Alois P. Heinz, Antidiagonals n = 0..20, flattened

Cf. A020449, A036929.

a(n, k) = i=0; forprime(p=10^(n+k-1), (10^(n+k)-1)/9, if(vecmax(digits(p))==1 && sumdigits(p)==k, return(p); i++; break)); if(i==0, return(0))
table(row, col) = for(x=0, row, for(y=2, col, print1(a(x, y), " ")); print(""))
table(4, 5) \\ print 5 X 4 table

More terms from Alois P. Heinz, Aug 17 2015

cp's OEIS Frontend

A157712 Smallest prime made up of 0's and prime(n) 1's (or 0 when no such prime exists).

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