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).

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

Offset: 1

Author

Jean-Marc Falcoz, Feb 19 2009

Keywords

• base
• nonn

Comments

The single-digit 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 single-digit terms. - M. F. Hasler, Jan 07 2015

A subset of the orderly Friedman numbers A080035. - M. F. Hasler, Jan 04 2015

Examples

			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".
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..423 (terms < 10^8)
• Giovanni Resta, Decompositions for terms < 10^8

Crossrefs

Cf. A036057, A080035, A252484.

Programs

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[i-1]==4&&next(2));n==eval(Strchr(v))&&return(1))}

Extensions

Edited by M. F. Hasler, Jan 04 2015