A258069 Nonnegative integers that can be computed using exactly eight 8's and the four basic arithmetic operations {+, -, *, /}.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92

Offset: 1

Author

Alois P. Heinz, May 18 2015

Keywords

• nonn
• fini
• full

Comments

The smallest non-computable number here is 91. The largest computable number here is 8^8 = 16777216.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1660

Crossrefs

Cf. A171826, A171827, A171828, A171829, A258068, A258070, A258071.

Cf. A182002, A258097.

Programs

Maple

f:= proc(n) f(n):= `if`(n=1, {8}, {seq(seq(seq([x+y, x-y, x*y,
      `if`(y=0, [][], x/y)][], y=f(n-j)), x=f(j)), j=1..n-1)})
    end:
sort([select(z->z>=0 and is(z, integer), f(8))[]])[];

PARI

A258069(n=8, S=Vec([[n]], n))={for(n=2, n, S[n]=Set(concat(vector(n\2, k, Set(concat([Set(concat([[T+U, T-U, U-T, if(U, T/U), if(T, U/T), T*U] | T <- S[n-k]])) | U <- S[k]])))))); select(t->t>=0 && type(t)=="t_INT", S[n])} \\ A258069() yields this sequence, use optional arg to compute variants. - M. F. Hasler, Nov 24 2018