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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
0, 1, 81, 441, 3721 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)