A181898 Smallest positive integer which cannot be calculated by an expression containing n binary operators (any of add, subtract, multiply and divide) whose operands are any integer between 1 and 9; parentheses allowed.

10, 19, 92, 417, 851, 4237, 14771, 73237, 298609

Offset

0,1

Links

Table of n, a(n) for n=0..8.

Derek M. Jones, R program for calculating values

Index to sequences related to the complexity of n

Example

a(2)=92 because at least 3 operators are required, e.g., (2*7 + 9)*4.

Mathematica

A181898[m_] := Module[{r = {Range[9]}, f, g}, f[A_, B_] := Union@Flatten@Outer[{#1 + #2, #1 - #2, #1 #2, If[#2 != 0 && Mod[#1, #2] == 0, #1/#2, Nothing]} &, A, B, 1]; g[S_] := First@Complement[Range[Max[S] + 1], Select[S, Positive]]; Print[0, " -> ", g@r[[1]]]; Do[Print[n, " -> ", g@Last@(r = Append[r, Union@Flatten@Table[f[r[[i + 1]], r[[n - i]]], {i, 0, n - 1}]])], {n, 1, m}]] (* Mike Sheppard, Feb 14 2026 *)

Prog

(R) See Jones link.
(PARI) first(n)=my(op=[(x, y)->x+y, (x, y)->x-y, (x, y)->y-x, (x, y)->x*y, (x, y)->x/y, (x, y)->y/x], v=vector(n+1), t); v[1]=[1..9]; for(k=2, #v, my(u=[]); for(i=1, (k+1)\2, my(a=v[i], b=v[k-i]); t=Set(concat(apply(f->setbinop(f, a, b), op))); u=concat(u, t)); v[k]=setminus(Set(u), [0])); t=10; for(i=1, #v, while(setsearch(v[i], t), t++); v[i]=t); v \\ Charles R Greathouse IV, Jan 09 2017

Crossrefs

Cf. A181957, A181958, A181959, A181960, A005520, A048183 (see text of comment).

Sequence in context: A007811 A255764 A181957 * A219688 A166706 A131495

Adjacent sequences: A181895 A181896 A181897 * A181899 A181900 A181901

Keyword

nonn

Author

Derek M. Jones, Apr 03 2012

Status

approved