A153751 Numbers k such that there are 15 digits in k^2 and for each factor f of 15 (1,3,5) the sum of digit groupings of size f is a square.

10000000, 10000001, 10000002, 10000003, 10000004, 10000005, 10000010, 10000011, 10000012, 10000013, 10000020, 10000021, 10000022, 10000030, 10000031, 10000200, 10000300, 10011003, 10022000, 10035990, 10042440

Offset: 1

Author

Doug Bell, Dec 31 2008

Keywords

• nonn
• base
• fini
• full

Comments

This sequence is a subsequence of both A153745 and A061910.

The last term is a(2782) = 31616301. - Giovanni Resta, Jun 06 2015

Examples

			10000011^2 = 100000220000121;
1+0+0+0+0+0+2+2+0+0+0+0+1+2+1 = 9 = 3^2;
100+000+220+000+121 = 441 = 21^2;
10000+02200+00121 = 12321 = 111^2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..2782 (all terms)

Crossrefs

Cf. A004159, A061910, A153745.

Programs

Mathematica

Select[Range[10^7,31622776],AllTrue[{Sqrt[Total[IntegerDigits[#^2]]],Sqrt[Total[ FromDigits/@ Partition[IntegerDigits[#^2],3]]],Sqrt[Total[FromDigits/@Partition[IntegerDigits[#^2],5]]]},IntegerQ]&] (* Harvey P. Dale, Apr 11 2023 *)