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A117678
Squares for which the multiplicative digital root is also a square.
2
0, 1, 4, 9, 25, 100, 169, 196, 225, 256, 400, 529, 576, 625, 676, 900, 961, 1024, 1089, 1156, 1225, 1296, 1521, 1600, 2025, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3481, 3600, 3844, 3969, 4096, 4225, 4356, 4489, 4900, 5041, 5184, 5329
OFFSET
1,3
COMMENTS
From Robert Israel, Oct 22 2015: (Start)
1, 9, and squares in A034048 and A034051.
Are there infinitely many squares in A034051? (End)
LINKS
MAPLE
A007954 := proc(n) return mul(d, d=convert(n, base, 10)): end: A117678 := proc(n) option remember: local k, m: if(n=1)then return 0:fi: for k from procname(n-1)+1 do m:=k^2: while(length(m)>1)do m:=A007954(m): od: if(m in {0, 1, 4, 9})then return k: fi: od: end: seq(A117678(n)^2, n=1..47); # Nathaniel Johnston, May 05 2011
MATHEMATICA
Select[Range[0, 73]^2, IntegerQ@ Sqrt[FixedPoint[Times @@ IntegerDigits@ # &, #] &@ #] &] (* Michael De Vlieger, Oct 22 2015 *)
PROG
(PARI) t(k) = {while(k>9, k=prod(i=1, #k=digits(k), k[i])); k}
for(n=0, 100, if(issquare(t(n^2)), print1(n^2, ", "))); \\ Altug Alkan, Oct 22 2015
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 12 2006
EXTENSIONS
Offset and some terms corrected by Nathaniel Johnston, May 05 2011
STATUS
approved