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A135027 Numbers k such that the sum of the digits of k^2 is 10. Multiples of 10 are omitted. 3
8, 19, 35, 46, 55, 71, 145, 152, 179, 251, 332, 361, 449, 451, 548, 649, 4499, 20249, 20251, 24499, 100549, 114499, 316261 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A subsequence of A056020. - R. J. Mathar, Feb 10 2008

Next term > 10000000. - R. J. Mathar, Oct 20 2009

If it exists, a(24) > 10^10. - Hugo Pfoertner, May 17 2021

If it exists, a(24) > 10^29. - Michael S. Branicky, May 30 2021

LINKS

Table of n, a(n) for n=1..23.

Michael S. Branicky, Python program

EXAMPLE

Corresponding squares are 64, 361, 1225, 2116, 3025, 5041, 21025, 23104, 32041, 63001, 110224, 130321, 201601, 203401, 300304, 421201, 20241001, 410022001, 410103001, 600201001, 10110101401, 13110021001, 100021020121.

8^2 = 64 and 6+4 = 10. 316261^2 = 100021020121 and 1+0+0+0+2+1+0+2+0+1+2+1 = 10. - Zak Seidov, Aug 26 2009

MATHEMATICA

s={}; Do[If[Mod[n, 10]>0&&10==Total[IntegerDigits[n^2]], AppendTo[s, n]], {n, 10^8}]; s (* Zak Seidov, Aug 26 2009 *)

PROG

(Python)

def A007953(n):

a=0

sh=n

while sh > 0:

a += sh % 10

sh //= 10

return a

def isA135027(n):

if n % 10 == 0:

return False

else:

return A007953(n**2) == 10

for n in range(70000):

if isA135027(n):

print(n)

# R. J. Mathar, Oct 20 2009

(Python) # See linked program to go to large numbers

def ok(n): return n%10 != 0 and sum(map(int, str(n*n))) == 10

print(list(filter(ok, range(316262)))) # Michael S. Branicky, May 30 2021

(PARI) is(n) = sumdigits(n^2)==10 && n%10 > 0 \\ Felix Fröhlich, May 17 2021

CROSSREFS

Cf. A007953, A056020.

Sequence in context: A140672 A230098 A262713 * A158916 A045557 A289877

Adjacent sequences: A135024 A135025 A135026 * A135028 A135029 A135030

KEYWORD

base,more,nonn

AUTHOR

Zak Seidov, Feb 10 2008

STATUS

approved

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Last modified January 28 21:40 EST 2023. Contains 359905 sequences. (Running on oeis4.)