A270538 Numbers n > 0 such that n = (d_1^1 + d_2^2 + d_3^3 + ...)^2, where d_k represents the k-th decimal digit of n.

0, 1, 81, 441, 3721

Offset

1,3

Comments

No other terms below 10^8.

All terms are square by definition.

No other terms below 4*10^18. - Chai Wah Wu, Apr 08 2016

Links

Table of n, a(n) for n=1..5.

Example

441 is a term because 441 = (4^1+4^2+1^3)^2;
3721 is a term because 3721 = (3^1+7^2+2^3+1^4)^2.

Mathematica

f[n_] := (Plus @@ (IntegerDigits[n]^Range[ Floor[ Log[10, n] + 1]]))^2; Select[ Range[10^4], f[ # ] == # &]
Select[Range[10^6]^2, With[{id=IntegerDigits[#]}, #==Sum[ id[[i]]^i, {i, Length[id]}]^2]&] (* Ray Chandler, Apr 01 2016 *)
Join[{0}, Select[Range[4000], Total[IntegerDigits[#]^Range[ IntegerLength[ #]]]^2 ==#&]] (* Harvey P. Dale, Aug 21 2019 *)

Prog

(PARI) isok(n) = my(d=digits(n)); n == sum(k=1, #d, d[k]^k)^2; \\ Michel Marcus, Mar 25 2016
(Python)
A270538_list = [n**2 for n in range(10**6) if n == sum(int(a)**(b+1) for b, a in enumerate(str(n**2)))] # Chai Wah Wu, Apr 08 2016

Crossrefs

Sequence in context: A237945 A237938 A017630 * A230064 A236710 A236705

Adjacent sequences: A270535 A270536 A270537 * A270539 A270540 A270541

Keyword

nonn,base,more

Author

José de Jesús Camacho Medina, Mar 18 2016

Status

approved