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

Author

Zak Seidov, Aug 17 2012

Keywords

• nonn
• base
• more

Comments

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

Crossrefs

Cf. A004159 (sum of digits of n^2).

Subsequence of A262711.

Cf. A384094 (similar for digit sum 9), A384095 (subset of "sporadic solutions").

Programs

Mathematica

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

PARI

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

Extensions

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