

A156954


Integers N such that by inserting + or  or * or / or ^ between each of their digits, without any grouping parentheses, you can get N (the ambiguous a^b^c is avoided).


3



736, 2592, 11664, 15617, 15618, 15622, 15624, 15632, 15642, 15645, 15656, 15662, 15667, 15698, 17536, 27639, 32785, 39363, 39369, 45947, 46633, 46644, 46648, 46655, 46660, 46663, 117635, 117638, 117639, 117642, 117643, 117647, 117650
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OFFSET

1,1


COMMENTS

The singledigit numbers 0, ..., 9 are here excluded by convention although they also ("voidly") satisfy the definition and therefore logically should be terms of this sequence. This is in contrast to the Friedman numbers A036057 where the construction also allows concatenation of digits but then of course has to exclude the case where only concatenation of the digits is used, which excludes the singledigit terms.  M. F. Hasler, Jan 07 2015


LINKS



EXAMPLE

736 = 7 + 3^6.
2592 = 2^5*9^2.
11664 = 1*1*6^6/4.
15617 = 1*5^6  1  7.
For more examples, see the link to "decompositions".


PROG

(PARI) is(n, o=Vecsmall("*+^/"))={v=Vecsmall(Str(n, n\10)); forstep(i=#v, 3, 2, v[i]=v[i\2+1]); n>9 && forvec(s=vector(#v\2, i, [1, #o(v[i*2+1]==48)]), for(i=1, #s, 94==(v[2*i]=o[s[i]])&&i>1&&s[i1]==4&&next(2)); n==eval(Strchr(v))&&return(1))}


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



