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%I #15 Aug 30 2018 17:16:21
%S 0,1,2,3,4,5,6,7,8,9,22,123,137,139,168,179,188,233,267,299,346,389,
%T 899,1124,1157,1347,1355,1469,1779,1788,2236,2346,2348,2778,3335,3779,
%U 11126,11133,11148,11177,11222,11238,11279,11339,11369,11579,11666,11677,11679,11699
%N Numbers with digits in nondecreasing order such that additive and multiplicative digital roots coincide.
%C A299690 can be used to find terms for this sequence below some bound by prepending ones to terms while staying below that bound so the additive and multiplicative root that term matches.
%C For example, 27 is in A299690 and has multiplicative root 4. 27 has the additive root 9. Prepending 4 ones gives the number 111127 which has multiplicative root 4, the same as 27 has, but it also has an additive root of 4. Furthermore, the digits are in nondecreasing order hence is in this sequence.
%o (PARI) is(n) = my(cn=n); d=digits(n); if(d!=vecsort(d), return(0)); while(cn>9, d=digits(cn); cn=prod(i=1, #d, d[i])); cn-1 == (n-1)%9 || n == 0
%Y Cf. A009994, A010888, A031347, A064702, A277061, A299690.
%K nonn,base
%O 1,3
%A _David A. Corneth_, Aug 23 2018