A034096 -id:A034096 - cp's OEIS frontend

A023961 First digit after decimal point of square root of n.

0, 4, 7, 0, 2, 4, 6, 8, 0, 1, 3, 4, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 0, 0, 0, 1, 1, 2

Offset: 1

N. J. A. Sloane, Olivier Gérard

When n is a square, a(n) is equal to 0, but the converse is not true, see A034096. - Michel Marcus, Sep 21 2015

			sqrt(1) = 1.00000000... hence a(1) = 0.
sqrt(2) = 1.41421356... hence a(2) = 4.
sqrt(3) = 1.73205080... hence a(3) = 7.
sqrt(4) = 2.00000000... hence a(4) = 0.
Note that 26 = 2 * 13 and sqrt(26) = 5.09901951... so a(26) = 0 even though 26 is not a perfect square.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A111862, A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111859.

A023961 := proc(n) return floor(10*sqrt(n)) mod 10: end: seq(A023961(n),n=1..100); # Nathaniel Johnston, May 04 2011

Array[Function[n, RealDigits[N[Power[n, 1/2], 10], 10] // (#[[1, #[[2]] + 1]]) &], 110]
fd[n_] := Module[{rd = RealDigits[Sqrt[n], 10, 10]}, First[rd][[Last[rd] + 1]]]; Array[fd, 90] (* Harvey P. Dale, Jan 16 2014 *)

a(n) = floor(10*sqrt(n)) % 10; \\ Michel Marcus, Sep 21 2015

a(n) = A010879(A000196(100*n)). - Robert Israel, Jul 30 2015

A034106 Fractional part of square root of n starts with 0: first term of runs (squares excluded).

Original entry on oeis.org

26, 37, 50, 65, 82, 101, 122, 145, 170, 197, 226, 257, 290, 325, 362, 401, 442, 485, 530, 577, 626, 677, 730, 785, 842, 901, 962, 1025, 1090, 1157, 1226, 1297, 1370, 1445, 1522, 1601, 1682, 1765, 1850, 1937, 2026, 2117, 2210, 2305, 2402, 2501, 2602

Offset: 1

Patrick De Geest, Sep 15 1998

Same as sequence A002522 (n^2+1) starting from the seventh term.

Cf. A034096.

A034309 Decimal part of a(n)^(1/3) starts with reversal of its integer part: first term of runs.

Original entry on oeis.org

11, 36, 86, 167, 288, 457, 682, 971, 1004, 1372, 1821, 2358, 2993, 3732, 4583, 5555, 6656, 7893, 8025, 9421, 10971, 12682, 14563, 16621, 18864, 21301, 23938, 26785, 27082, 30168, 33480, 37026, 40815, 44853, 49149, 53711, 58547, 63665, 64193

Offset: 0

Patrick De Geest, Oct 15 1998

Harvey P. Dale, Table of n, a(n) for n = 0..100

Cf. A034096-A034135.

dp3Q[n_]:=Module[{il=IntegerLength[Floor[CubeRoot[n]]],c},c=TakeDrop[RealDigits[ CubeRoot[ n],10,2il][[1]],il];c[[1]]==Reverse[c[[2]]]]; Split[Select[Range[65000], dp3Q], (#2 - #1 == 1 &)][[;; , 1]] (* Harvey P. Dale, May 26 2024 *)

A034308 Decimal part of a(n)^(1/2) starts with reversal of its integer part: first term of runs.

Original entry on oeis.org

5, 11, 20, 31, 44, 60, 78, 99, 276, 354, 401, 494, 544, 709, 831, 902, 1039, 1111, 1186, 1263, 1342, 1424, 1508, 1595, 1604, 1693, 1785, 1879, 1975, 2074, 2176, 2280, 2386, 2495, 2506, 2617, 2731, 2847, 2965, 3086, 3210, 3336, 3464, 3595, 3608, 3741, 3877

Offset: 0

Patrick De Geest, Oct 15 1998

Cf. A034096-A034135.

A034310 Decimal part of a(n)^(1/4) starts with reversal of its integer part: first term of runs.

Original entry on oeis.org

2, 24, 119, 375, 916, 1898, 3516, 5997, 9606, 10041, 15236, 22227, 31385, 43118, 57870, 76117, 98373, 125186, 157140, 160641, 198965, 243768, 295743, 355618, 424154, 502149, 590437, 689884, 801395, 813245, 939111, 1079050, 1234075

Offset: 0

Patrick De Geest, Oct 15 1998

Cf. A034096-A034135.

A034311 Decimal part of a(n)^(1/5) starts with reversal of its integer part: first term of runs.

Original entry on oeis.org

2, 52, 392, 1650, 5033, 12524, 27068, 52774, 95100, 100502, 169267, 271381, 417725, 621327, 897551, 1264295, 1742180, 2354746, 3128646, 3216033, 4202131, 5416520, 6896723, 8684170, 10824388, 13367195, 16366889, 19882450, 23977724

Offset: 0

Patrick De Geest, Oct 15 1998

Cf. A034096-A034135.

A034312 Decimal part of a(n)^(1/6) starts with reversal of its integer part: first term of runs.

Original entry on oeis.org

2, 114, 1292, 7257, 27681, 82654, 208423, 464405, 941481, 1006016, 1880548, 3313554, 5559918, 8953316, 13921012, 20999928, 30853993, 44292764, 62291324, 64384962, 88749004, 120355053, 160831561, 212067423, 276238382, 355834709

Offset: 0

Patrick De Geest, Oct 15 1998

Cf. A034096-A034135.

A034313 Decimal part of a(n)^(1/7) starts with reversal of its integer part: first term of runs.

Original entry on oeis.org

2, 250, 4262, 31928, 152244, 545517, 1604853, 4086756, 9320654, 10070211, 20892885, 40458488, 74002500, 129017276, 215914886, 348808796, 546424205, 833146874, 1240220256, 1288986925, 1874378945, 2674289273, 3750591998

Offset: 0

Patrick De Geest, Oct 15 1998

Cf. A034096-A034135.

A034314 Decimal part of a(n)^(1/8) starts with reversal of its integer part: first term of runs.

Original entry on oeis.org

3, 549, 14065, 140483, 837340, 3600407, 12357363, 35963453, 92274470, 100802806, 232119952, 493998138, 984973268, 1859138937, 3348839878, 5793714089, 9677172654, 15671492689, 24692785296, 25805518236, 39586883307

Offset: 0

Patrick De Geest, Oct 15 1998

Cf. A034096-A034135.

A034315 Decimal part of a(n)^(1/9) starts with reversal of its integer part: first term of runs.

Original entry on oeis.org

3, 1208, 46412, 618122, 4605367, 23762681, 95151695, 316478382, 913517248, 1009036085, 2578852664, 6031717260, 13109994192, 26790192075, 51940506497, 96233591016, 171382727700, 294780777472, 491633355232, 516626475073

Offset: 0

Patrick De Geest, Oct 15 1998

Cf. A034096-A034135.

cp's OEIS Frontend

A023961 First digit after decimal point of square root of n.

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A034106 Fractional part of square root of n starts with 0: first term of runs (squares excluded).

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A034309 Decimal part of a(n)^(1/3) starts with reversal of its integer part: first term of runs.

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A034308 Decimal part of a(n)^(1/2) starts with reversal of its integer part: first term of runs.

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A034310 Decimal part of a(n)^(1/4) starts with reversal of its integer part: first term of runs.

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A034311 Decimal part of a(n)^(1/5) starts with reversal of its integer part: first term of runs.

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A034312 Decimal part of a(n)^(1/6) starts with reversal of its integer part: first term of runs.

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A034313 Decimal part of a(n)^(1/7) starts with reversal of its integer part: first term of runs.

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A034314 Decimal part of a(n)^(1/8) starts with reversal of its integer part: first term of runs.

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A034315 Decimal part of a(n)^(1/9) starts with reversal of its integer part: first term of runs.

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