A117678 Squares for which the multiplicative digital root is also a square.

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, 5476, 5625

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)

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 422.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

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

Cf. A000290, A031347, A034048, A034051, A116978.

Sequence in context: A237613 A220444 A355799 * A167045 A262753 A055851

Adjacent sequences: A117675 A117676 A117677 * A117679 A117680 A117681

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