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

0,1

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.

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A020449, A036929.

Sequence in context: A185682 A217752 A335646 * A287468 A110417 A240560

Adjacent sequences: A261170 A261171 A261172 * A261174 A261175 A261176

Keyword

nonn,tabl,base

Author

Felix Fröhlich, Aug 10 2015

Extensions

More terms from Alois P. Heinz, Aug 17 2015

Status

approved