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Numbers whose square starts with 5 identical digits.
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10541, 33334, 47141, 57735, 66667, 105409, 105410, 105411, 105412, 105413, 149071, 149072, 149073, 182574, 182575, 182576, 210818, 210819, 235702, 235703, 258198, 258199, 278886, 278887, 298141, 298142, 316227, 333332, 333333, 333334
Smallest number whose n-th power begins with precisely n identical digits (in base ten).
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1, 15, 322, 167, 6444, 32183, 7306, 225418, 6551032, 683405939, 7074698775, 26331754107, 844494314469, 11303028458639, 251188643150958, 93364101391902, 16114920282762613, 239390020079624346, 191165654339590395
Numbers whose square starts with 4 identical digits.
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4
2357, 2582, 3334, 4714, 5774, 6667, 8165, 8819, 9428, 10541, 10542, 10543, 10544, 10545, 14907, 14908, 14909, 18257, 18258, 18259, 21081, 21082, 21083, 23570, 23571, 25819, 25820, 27888, 27889, 29813, 29814, 31622, 33332, 33333
a(n) = the smallest positive number, not ending in 0, whose square has a substring of exactly n identical digits.
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1
1, 12, 38, 1291, 10541, 57735, 364585, 1197219, 50820359, 169640142, 298142397, 4472135955, 1490711985, 2185812841434
Positive numbers whose square starts with exactly 3 identical digits.
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149, 298, 334, 472, 667, 745, 882, 1054, 1055, 1056, 1057, 1058, 1490, 1491, 1492, 1493, 1825, 1826, 1827, 2108, 2109, 2356, 2581, 2788, 2789, 2980, 2981, 3161, 3162, 3332, 3333, 3335, 3336, 3337, 3338, 3339, 3340, 3341, 3342, 3343, 3344, 3345, 3346
COMMENTS
2357 is the first term of A131573 that is not in this sequence (see Example section), the next ones are 2582, 3334, ...
Numbers whose square starts with exactly 4 identical digits.
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2357, 2582, 3334, 4714, 5774, 6667, 8165, 8819, 9428, 10542, 10543, 10544, 10545, 14907, 14908, 14909, 18257, 18258, 18259, 21081, 21082, 21083, 23570, 23571, 25819, 25820, 27888, 27889, 29813, 29814, 31622, 33332, 33333, 33335, 33336, 33337, 33338, 33339, 33340, 33341, 33342
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