A178224 Numbers k such that d(1)^1 + d(2)^2 +... + d(p)^p is a square, where d(i), i=1..p, are the decimal digits of k.

0, 1, 4, 9, 10, 31, 40, 52, 73, 81, 90, 94, 100, 102, 142, 144, 148, 163, 211, 247, 301, 310, 345, 352, 400, 421, 422, 466, 520, 523, 526, 562, 573, 631, 643, 679, 711, 712, 730, 772, 785, 801, 802, 810, 813, 816, 832, 834, 838, 841, 865, 874, 877, 900, 903, 906, 937, 940, 982, 983, 986, 1000, 1020, 1022, 1042, 1082, 1111, 1172, 1420

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

8762 is in the sequence because 8 + 7^2 + 6^3 + 2^4 = 289 = 17^2.

Maple

with(numtheory):for n from 0 to 1500 do:l:=length(n):n0:=n:s:=0:for m from
  1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+u^(l-m+1):od:if type(sqrt(s), integer)=true  then printf(`%d, `, n):else fi:od:

Mathematica

sqQ[n_]:=Module[{idn=IntegerDigits[n]}, IntegerQ[Sqrt[Total[idn^Range[ Length[ idn]]]]]]; Select[Range[0, 1500], sqQ] (* Harvey P. Dale, Jun 22 2011 *)

Prog

(Sage) is_A178224 = lambda x: is_square(sum(d**i for i, d in enumerate(reversed(x.digits()), 1))) # D. S. McNeil, Dec 20 2010

Crossrefs

Sequence in context: A236024 A141395 A121215 * A102985 A112401 A178360

Adjacent sequences: A178221 A178222 A178223 * A178225 A178226 A178227

Keyword

nonn,base

Author

Michel Lagneau, Dec 20 2010

Extensions

Offset corrected by Robert Israel, Feb 19 2024

Status

approved