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A153751
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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.
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2
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10000000, 10000001, 10000002, 10000003, 10000004, 10000005, 10000010, 10000011, 10000012, 10000013, 10000020, 10000021, 10000022, 10000030, 10000031, 10000200, 10000300, 10011003, 10022000, 10035990, 10042440
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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STATUS
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approved
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