cp's OEIS Frontend

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).

%I A156954 #26 Jan 14 2021 21:15:20
%S A156954 736,2592,11664,15617,15618,15622,15624,15632,15642,15645,15656,15662,
%T A156954 15667,15698,17536,27639,32785,39363,39369,45947,46633,46644,46648,
%U A156954 46655,46660,46663,117635,117638,117639,117642,117643,117647,117650
%N 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).
%C A156954 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
%C A156954 A subset of the orderly Friedman numbers A080035. - _M. F. Hasler_, Jan 04 2015
%H A156954 Giovanni Resta, <a href="/A156954/b156954.txt">Table of n, a(n) for n = 1..423</a> (terms < 10^8)
%H A156954 Giovanni Resta, <a href="/A156954/a156954.txt">Decompositions for terms < 10^8</a>
%e A156954 736 = 7 + 3^6.
%e A156954 2592 = 2^5*9^2.
%e A156954 11664 = 1*1*6^6/4.
%e A156954 15617 = 1*5^6 - 1 - 7.
%e A156954 For more examples, see the link to "decompositions".
%o A156954 (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))}
%Y A156954 Cf. A036057, A080035, A252484.
%K A156954 base,nonn
%O A156954 1,1
%A A156954 _Jean-Marc Falcoz_, Feb 19 2009
%E A156954 Edited by _M. F. Hasler_, Jan 04 2015