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.

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

Author

Felix Fröhlich, Aug 10 2015

Keywords

• nonn
• tabl
• base

Comments

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A020449, A036929.

Programs

PARI

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

Extensions

More terms from Alois P. Heinz, Aug 17 2015