A045860 -id:A045860 - cp's OEIS frontend

A045789 Squares with initial digit '6'.

64, 625, 676, 6084, 6241, 6400, 6561, 6724, 6889, 60025, 60516, 61009, 61504, 62001, 62500, 63001, 63504, 64009, 64516, 65025, 65536, 66049, 66564, 67081, 67600, 68121, 68644, 69169, 69696, 600625, 602176, 603729, 605284, 606841

Offset: 1

Jeff Burch

Cf. A045860.

Cf. A045784, A045785, A045786, A045787, A045788, A045791, A045792, A045793.

Flatten[Table[Range[Ceiling[Sqrt[6 10^n]],Floor[Sqrt[7 10^n]]]^2,{n,5}]] (* Harvey P. Dale, Jun 15 2011 *)

a(n) = A045860(n)^2. - Michel Marcus, Sep 04 2021

A035073 a(n) is root of square starting with digit 6: first term of runs.

Original entry on oeis.org

8, 25, 78, 245, 775, 2450, 7746, 24495, 77460, 244949, 774597, 2449490, 7745967, 24494898, 77459667, 244948975, 774596670, 2449489743, 7745966693, 24494897428, 77459666925, 244948974279, 774596669242, 2449489742784, 7745966692415, 24494897427832, 77459666924149

Offset: 1

Patrick De Geest, Nov 15 1998

Subsequence of A045860.

Cf. A067576 (squares), A035076 (2..9).

from math import isqrt
def a(n): return isqrt(6*10**n) + 1
print([a(n) for n in range(1, 28)]) # Michael S. Branicky, Aug 25 2021

a(n) = ceiling(sqrt(6*10^n)), n > 0.

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

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A045789 Squares with initial digit '6'.

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A035073 a(n) is root of square starting with digit 6: first term of runs.

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

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