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%I #8 Jul 09 2019 14:19:36
%S 0,1,2,3,4,5,6,7,8,9,736,15642,15662,1680129,1686394
%N Numbers n with odd length such that n = d_1+(d_2^d_3)+ ...+(d_(k-1)^d_k) where d_1 d_2 ... d_k is the decimal expansion of n.
%e 1686394 is in the sequence (the largest term) because 1686394=1+(6^8)+(6^3)+(9^4).
%t Do[h=IntegerDigits[n]; k=Length[h]; If[ OddQ[k] && Select[ Range[k/2], h[[2# ]] ==0== h[[2#+1]] &]=={} && n==h[[1]]+ Sum[h[[2j]]^h[[2j+1]], {j, k/2}], Print[n]], {n, 10^9}]
%t olQ[n_]:=Module[{idn=IntegerDigits[n],d2},d2=Partition[Rest[idn],2];OddQ[ Length[ idn]]&&FreeQ[d2[[All,2]],0]&&Total[#[[1]]^#[[2]]&/@d2]+ idn[[1]] == n]; Join[{0},Select[Range[169*10^4],olQ]] (* _Harvey P. Dale_, Jul 09 2019 *)
%Y Cf. A112015, A112016.
%K base,fini,full,nonn
%O 1,3
%A _Farideh Firoozbakht_, Sep 15 2005
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