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A309883 Numbers k such that A003132(k^2) = A003132(k), where A003132(n) is the sum of the squares of the digits of n. 1
0, 1, 10, 35, 100, 152, 350, 377, 452, 539, 709, 1000, 1299, 1398, 1439, 1519, 1520, 1569, 1591, 1679, 1965, 2599, 2838, 3332, 3500, 3598, 3770, 4520, 4586, 4754, 4854, 5390, 5501, 5835, 5857, 6388, 6595, 6735, 6861, 6951, 7090, 7349, 7887, 8395, 9795, 10000, 10056, 10159, 10389, 11055, 11091, 12990, 12999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If k is in the sequence, then so are k*10^r, r >= 1.

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

377^2 = 142129, A003132(377) = 3^2 + 7^2 + 7^2 = 107, A003132(142129) = 1^2 + 4^2 + 2^2 + 1^2 + 2^2 + 9^2 = 107.

MATHEMATICA

digSum[n_] := Total[IntegerDigits[n]^2]; Select[Range[0, 13000], digSum[#] == digSum[#^2] &] (* Amiram Eldar, Aug 22 2019 *)

PROG

(PARI) for(i = 0, 30000, if(norml2(digits(i^2)) == norml2(digits(i)), print1(i, ", ")))

(Python)

def A003132(n):

    s = 0

    while n > 0:

        s, n = s+(n%10)**2, n//10

    return s

n, a = 0, 0

while n < 50:

    if A003132(a) == A003132(a*a):

        n = n+1

        print(n, a)

    a = a+1 # A.H.M. Smeets, Aug 23 2019

(MAGMA) [0] cat [k:k in [1..13000]| &+[c^2: c in Intseq(k)] eq &+[c^2: c in Intseq(k^2)]]; // Marius A. Burtea, Aug 24 2019

CROSSREFS

Cf. A003132, A058369, A070276, A174460, A176670, A178213, A307735, A309884.

Sequence in context: A000447 A052472 A272352 * A049736 A048507 A240267

Adjacent sequences:  A309880 A309881 A309882 * A309884 A309885 A309886

KEYWORD

nonn,base

AUTHOR

Antonio Roldán, Aug 21 2019

STATUS

approved

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Last modified November 21 12:20 EST 2019. Contains 329370 sequences. (Running on oeis4.)