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A228187 Positive numbers which when decremented by the product of their digits produce a square.

%I A228187 #24 Aug 16 2025 14:00:37
%S A228187 1,2,3,4,5,6,7,8,9,24,37,45,48,67,71,79,100,228,231,256,259,292,388,
%T A228187 400,524,575,624,661,832,865,868,900,928,949,973,985,1024,1089,1231,
%U A228187 1317,1344,1399,1541,1549,1564,1600,1612,1629,1723,1759,2025,2164,2209
%N A228187 Positive numbers which when decremented by the product of their digits produce a square.
%H A228187 Alois P. Heinz, <a href="/A228187/b228187.txt">Table of n, a(n) for n = 1..1000</a>
%e A228187 388 is a term because 388-(3*8*8) = 196 = 14^2.
%p A228187 a:= proc(n) option remember; local d, k, m;
%p A228187       for k from 1+`if`(n=1, 0, a(n-1)) do
%p A228187         d, m:= 1, k;
%p A228187         while m>0 do d:=d*irem(m,10,'m') od;
%p A228187         if issqr(k-d) then return k fi
%p A228187       od
%p A228187     end:
%p A228187 seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 19 2013
%t A228187 Select[Range[2500],IntegerQ[Sqrt[#-Times@@IntegerDigits[#]]]&] (* _Harvey P. Dale_, Aug 16 2025 *)
%o A228187 (PARI) for(n=0,10^4,d=digits(n);p=prod(i=1,#d,d[i]);if(issquare(n-p),print(n,", "))) \\ _Derek Orr_, Mar 13 2015
%Y A228187 Cf. A066567.
%K A228187 base,nonn,easy
%O A228187 1,2
%A A228187 _Derek Orr_, Aug 15 2013