A262711 -id:A262711 - cp's OEIS frontend

A215614 Numbers k that are not multiples of 10 and such that sum of digits of k^2 is 7.

4, 5, 32, 49, 149, 1049

Offset: 1

Zak Seidov, Aug 17 2012

Except for the number 1, the terms of this sequence and numbers 10^k+1 (A062397) are the only numbers (up to trailing 0's) whose square has sum of digits less than 9. - M. F. Hasler, Sep 23 2014
Is this sequence finite? See also A384095 for a similar problem with digit sum 9. - M. F. Hasler, Jun 20 2025
a(7) > 10^15 if it exists. - David A. Corneth, Jun 21 2025
a(7) > 10^65 if it exists. - Michael S. Branicky, Jun 25 2025
a(7) > 10^700 if it exists. - Max Alekseyev, Jun 27 2025

Cf. A004159 (sum of digits of n^2).
Subsequence of A262711.
Cf. A384094 (similar for digit sum 9), A384095 (subset of "sporadic solutions").

Select[Range[1500],Mod[#,10]!=0&&Total[IntegerDigits[#^2]]==7&] (* Harvey P. Dale, Aug 21 2022 *)

for(n=1,9e9, n%10&&sumdigits(n^2)==7&&print1(n",")) \\ M. F. Hasler, Sep 23 2014

Edited and unproven keywords fini,full removed by Max Alekseyev, Jun 20 2025

A262712 Numbers k such that sum of digits of k^2 is 9.

Original entry on oeis.org

3, 6, 9, 12, 15, 18, 21, 30, 39, 45, 48, 51, 60, 90, 102, 105, 111, 120, 150, 180, 201, 210, 249, 300, 318, 321, 348, 351, 390, 450, 480, 501, 510, 549, 600, 900, 1002, 1005, 1011, 1020, 1050, 1101, 1110, 1149, 1200, 1500, 1761, 1800, 2001, 2010, 2100, 2490

Offset: 1

Vincenzo Librandi, Sep 28 2015

Subsequence of A008585.

			6 is in sequence because 6^2 = 36 and 3+6 = 9.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. similar sequences listed in A262711.

Cf. A004159, A008585, A061910.

[n: n in [1..2*10^4] | &+Intseq(n^2) eq 9 ];

filter:= proc(n) convert(convert(n^2,base,10),`+`) = 9 end proc:select(filter, [$1..10^5]); # Robert Israel, Jan 04 2024

Select[Range[10^5], Total[IntegerDigits[#^2]] == 9 &]

for(n=1, 1e8, if (sumdigits(n^2) == 9, print1(n", "))) \\ Altug Alkan, Sep 28 2015

A262713 Numbers k such that the sum of digits of k^2 is 10.

Original entry on oeis.org

8, 19, 35, 46, 55, 71, 80, 145, 152, 179, 190, 251, 332, 350, 361, 449, 451, 460, 548, 550, 649, 710, 800, 1450, 1520, 1790, 1900, 2510, 3320, 3500, 3610, 4490, 4499, 4510, 4600, 5480, 5500, 6490, 7100, 8000, 14500, 15200, 17900, 19000, 20249, 20251, 24499

Offset: 1

Vincenzo Librandi, Sep 28 2015

From Altug Alkan, Sep 29 2015: (Start)
Subsequence of A001651.
If a(n)+1 mod 9 != 0 then a(n)-1 mod 9 = 0;
if a(n)-1 mod 9 != 0 then a(n)+1 mod 9 = 0;
a(n)^2 - 1 mod 9 = 0. (End)
A135027(n)*10^k is a term for all n > 0, k >= 0. - Michael S. Branicky, Aug 19 2021

			19 is in sequence because 19^2 = 361 and 3+6+1 = 10.

Michael S. Branicky, Table of n, a(n) for n = 1..244
Michael S. Branicky, Python program

Cf. similar sequences listed in A262711.

Cf. A004159, A061910, A135027.

[n: n in [1..3*10^4] | &+Intseq(n^2) eq 10 ];

Select[Range[10^5], Total[IntegerDigits[#^2]] == 10 &]

for(n=1, 1e6, if (sumdigits(n^2) == 10, print1(n", "))) \\ Altug Alkan, Sep 28 2015

# See linked program to go to larger numbers
def ok(n): return sum(map(int, str(n*n))) == 10
print(list(filter(ok, range(25000)))) # Michael S. Branicky, Aug 19 2021

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A215614 Numbers k that are not multiples of 10 and such that sum of digits of k^2 is 7.

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A262712 Numbers k such that sum of digits of k^2 is 9.

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A262713 Numbers k such that the sum of digits of k^2 is 10.

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Author

Keywords

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Programs

Magma

Mathematica

PARI

Python