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

1, 2, 3, 4, 5, 6, 7, 8, 9, 24, 37, 45, 48, 67, 71, 79, 100, 228, 231, 256, 259, 292, 388, 400, 524, 575, 624, 661, 832, 865, 868, 900, 928, 949, 973, 985, 1024, 1089, 1231, 1317, 1344, 1399, 1541, 1549, 1564, 1600, 1612, 1629, 1723, 1759, 2025, 2164, 2209

Offset: 1

Author

Derek Orr, Aug 15 2013

Keywords

• base
• nonn
• easy

Examples

			388 is a term because 388-(3*8*8) = 196 = 14^2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066567.

Programs

Maple

a:= proc(n) option remember; local d, k, m;
      for k from 1+`if`(n=1, 0, a(n-1)) do
        d, m:= 1, k;
        while m>0 do d:=d*irem(m,10,'m') od;
        if issqr(k-d) then return k fi
      od
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 19 2013

Mathematica

Select[Range[2500],IntegerQ[Sqrt[#-Times@@IntegerDigits[#]]]&] (* Harvey P. Dale, Aug 16 2025 *)

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