A045789 -id:A045789 - cp's OEIS frontend

A045784 Squares with initial digit '1'.

1, 16, 100, 121, 144, 169, 196, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 10000, 10201, 10404, 10609, 10816, 11025, 11236, 11449, 11664, 11881, 12100, 12321, 12544, 12769, 12996, 13225, 13456, 13689, 13924

Offset: 1

Jeff Burch

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Cf. A045855.

Cf. A045785, A045786, A045787, A045788, A045789, A045791, A045792, A045793.

Select[Range[120]^2,First[IntegerDigits[#]]==1&] (* Harvey P. Dale, Dec 31 2011 *)

a(n) = A045855(n)^2. - Michel Marcus, Sep 04 2021

A045788 Squares with initial digit '5'.

Original entry on oeis.org

529, 576, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 50176, 50625, 51076, 51529, 51984, 52441, 52900, 53361, 53824, 54289, 54756, 55225, 55696, 56169, 56644, 57121, 57600, 58081, 58564, 59049, 59536, 501264, 502681, 504100, 505521

Offset: 1

Jeff Burch

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A045784, A045785, A045786, A045787, A045789, A045791, A045792, A045793.

seq(op(map(`^`, [seq(i,i=ceil(sqrt(5*10^d))..floor(sqrt(6*10^d-1)))],2)),d=1..5); # Robert Israel, Sep 30 2016

Flatten[Table[Range[Ceiling[Sqrt[5 10^n]],Floor[Sqrt[6 10^n]]]^2,{n,5}]]  (* Harvey P. Dale, Jun 15 2011 *)

a(n) = A045859(n)^2. - R. J. Mathar, Jul 23 2025

Offset changed by Robert Israel, Sep 30 2016

A045787 Squares with initial digit '4'.

Original entry on oeis.org

4, 49, 400, 441, 484, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 40000, 40401, 40804, 41209, 41616, 42025, 42436, 42849, 43264, 43681, 44100, 44521, 44944, 45369, 45796, 46225, 46656, 47089, 47524, 47961, 48400, 48841, 49284, 49729, 400689

Offset: 1

Jeff Burch

Cf. A045858.

Cf. A045784, A045785, A045786, A045788, A045789, A045791, A045792, A045793.

Flatten[Table[Range[Ceiling[Sqrt[4 10^n]],Floor[Sqrt[5 10^n]]]^2, {n,5}]] (* Harvey P. Dale, Jun 15 2011 *)

a(n) = A045858(n)^2. - Michel Marcus, Sep 04 2021

A045785 Squares with initial digit '2'.

Original entry on oeis.org

25, 225, 256, 289, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 20164, 20449, 20736, 21025, 21316, 21609, 21904, 22201, 22500, 22801, 23104, 23409, 23716, 24025, 24336, 24649, 24964, 25281, 25600, 25921, 26244, 26569

Offset: 1

Jeff Burch

Cf. A045856.

Cf. A045784, A045786, A045787, A045788, A045789, A045791, A045792, A045793.

Flatten[Table[Range[Ceiling[Sqrt[2 10^n]],Floor[Sqrt[3 10^n]]]^2,{n,4}]](* Harvey P. Dale, Jun 15 2011 *)

a(n) = A045856(n)^2. - Michel Marcus, Sep 04 2021

A045786 Squares with initial digit '3'.

Original entry on oeis.org

36, 324, 361, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969, 30276, 30625, 30976, 31329, 31684, 32041, 32400, 32761, 33124, 33489, 33856, 34225, 34596, 34969, 35344, 35721, 36100, 36481, 36864, 37249, 37636, 38025, 38416, 38809

Offset: 1

Jeff Burch

Cf. A045857.

Cf. A045784, A045785, A045787, A045788, A045789, A045791, A045792, A045793.

Select[Range[200]^2,First[IntegerDigits[#]]==3&]  (* Harvey P. Dale, Apr 21 2011 *)

a(n) = A045857(n)^2. - Michel Marcus, Sep 04 2021

A045791 Squares with initial digit '7'.

Original entry on oeis.org

729, 784, 7056, 7225, 7396, 7569, 7744, 7921, 70225, 70756, 71289, 71824, 72361, 72900, 73441, 73984, 74529, 75076, 75625, 76176, 76729, 77284, 77841, 78400, 78961, 79524, 700569, 702244, 703921, 705600, 707281, 708964, 710649, 712336

Offset: 1

Jeff Burch

Cf. A045861.

Cf. A045784, A045785, A045786, A045787, A045788, A045789, A045792, A045793.

Flatten[Table[Range[Ceiling[Sqrt[7 10^n]],Floor[Sqrt[8 10^n]]]^2,{n,5}]] (* Harvey P. Dale, Jun 15 2011 *)

a(n) = A045861(n)^2. - Michel Marcus, Sep 04 2021

A045792 Squares with initial digit '8'.

Original entry on oeis.org

81, 841, 8100, 8281, 8464, 8649, 8836, 80089, 80656, 81225, 81796, 82369, 82944, 83521, 84100, 84681, 85264, 85849, 86436, 87025, 87616, 88209, 88804, 89401, 801025, 802816, 804609, 806404, 808201, 810000, 811801, 813604, 815409, 817216

Offset: 1

Jeff Burch

Cf. A045862.

Cf. A045784, A045785, A045786, A045787, A045788, A045789, A045791, A045793.

a(n) = A045862(n)^2. - Michel Marcus, Sep 04 2021

a(16) corrected by Sean A. Irvine, Mar 21 2021

Offset 1 from Michel Marcus, Mar 22 2021

A045793 Squares with initial digit '9'.

Original entry on oeis.org

9, 900, 961, 9025, 9216, 9409, 9604, 9801, 90000, 90601, 91204, 91809, 92416, 93025, 93636, 94249, 94864, 95481, 96100, 96721, 97344, 97969, 98596, 99225, 99856, 900601, 902500, 904401, 906304, 908209, 910116, 912025, 913936, 915849

Offset: 1

Jeff Burch

Cf. A045863.

Cf. A045784, A045785, A045786, A045787, A045788, A045789, A045791, A045792.

Select[Range[1000]^2,First[IntegerDigits[#]]==9&] (* Harvey P. Dale, Apr 21 2015 *)

a(n) = A045863(n)^2. - Michel Marcus, Sep 04 2021

A045860 Numbers whose square has initial digit '6'.

Original entry on oeis.org

8, 25, 26, 78, 79, 80, 81, 82, 83, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799

Offset: 1

Jeff Burch

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Supersequence of A035073.

Cf. A045789.

Flatten[Table[Range[Ceiling[Sqrt[6*10^n]],Floor[Sqrt[7*10^n]]],{n,5}]] (* Harvey P. Dale, Apr 03 2013 *)

from math import isqrt
def aupto(limit):
    alst, d, end = [], 1, 0
    while end < limit:
        start, end = isqrt(6*10**d) + 1, isqrt(7*10**d-1)
        alst.extend([an for an in list(range(start, end+1)) if an <= limit])
        d += 1
    return alst
print(aupto(799)) # Michael S. Branicky, Aug 25 2021

A348490 Positive numbers whose square starts and ends with exactly one 6.

Original entry on oeis.org

26, 246, 254, 256, 264, 776, 784, 786, 794, 796, 804, 806, 824, 826, 834, 836, 2454, 2456, 2464, 2466, 2474, 2476, 2484, 2486, 2494, 2496, 2504, 2506, 2514, 2516, 2524, 2526, 2534, 2536, 2544, 2546, 2554, 2556, 2564, 2566, 2594, 2596, 2604, 2606, 2614, 2616, 2624, 2626, 2634, 2636, 2644, 7746

Offset: 1

Bernard Schott, Oct 29 2021

When a square ends with 6, it ends with only one 6.
From Marius A. Burtea, Oct 30 2021 : (Start)
The sequence is infinite because the numbers 806, 8006, 80006, ..., 8*10^k + 6, k >= 2, are terms with squares 649636, 64096036, 6400960036, 640009600036, ..., 64*10^(2*k) + 96*10^k + 36, k >= 2.
Numbers 796, 7996, 79996, 799996, 7999996, 79999996, ..., 10^k*8 - 4, k >= 2, are terms and have no digits 0, because their squares are 633616, 63936016, 6399360016, 639993600016, 63999936000016, 6399999360000016, ....
Also 794, 7994, 79994, 799994, ..., (8*10^k - 6), k >= 2, are terms and have no digits 0, because their squares are 630436, 63904036, 6399040036, 639990400036, 63999904000036, 6399999040000036, ... (End)

			26^2 = 676, hence 26 is a term.
814^2 = 662596, hence 814 is not a term.

Cf. A045789, A045860, A273373 (squares ending with 6).
Similar to: A348487 (k=1), A348488 (k=4), A348489 (k=5), this sequence (k=6), A348491 (k=9).
Subsequence of A305719.

[n:n in [4..7500]|Intseq(n*n)[1] eq 6 and Intseq(n*n)[#Intseq(n*n)] eq 6 and Intseq(n*n)[-1+#Intseq(n*n)] ne 6 ]; // Marius A. Burtea, Oct 30 2021

Select[Range[10, 7750], (d = IntegerDigits[#^2])[[1]] == d[[-1]] == 6 && d[[2]] != 6 &] (* Amiram Eldar, Oct 30 2021 *)

isok(k) = my(d=digits(sqr(k))); (d[1]==6) && (d[#d]==6) && if (#d>2, (d[2]!=6) && (d[#d-1]!=6), 1); \\ Michel Marcus, Oct 30 2021

from itertools import count, takewhile
def ok(n):
  s = str(n*n); return len(s.rstrip("6")) == len(s.lstrip("6")) == len(s)-1
def aupto(N):
  r = takewhile(lambda x: x<=N, (10*i+d for i in count(0) for d in [4, 6]))
  return [k for k in r if ok(k)]
print(aupto(2644)) # Michael S. Branicky, Oct 29 2021

cp's OEIS Frontend

A045784 Squares with initial digit '1'.

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A045788 Squares with initial digit '5'.

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A045787 Squares with initial digit '4'.

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A045785 Squares with initial digit '2'.

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A045786 Squares with initial digit '3'.

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A045791 Squares with initial digit '7'.

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A045792 Squares with initial digit '8'.

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A045793 Squares with initial digit '9'.

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A045860 Numbers whose square has initial digit '6'.

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A348490 Positive numbers whose square starts and ends with exactly one 6.

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