A045859 -id:A045859 - cp's OEIS frontend

A045788 Squares with initial digit '5'.

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

A348489 Positive numbers whose square starts and ends with exactly one 5.

Original entry on oeis.org

75, 225, 715, 725, 735, 755, 765, 2245, 2255, 2265, 2275, 2285, 2295, 2305, 2315, 2325, 2335, 2345, 2375, 2385, 2395, 2405, 2415, 2425, 2435, 2445, 7075, 7085, 7095, 7105, 7115, 7125, 7135, 7145, 7155, 7165, 7175, 7185, 7195, 7205, 7215, 7225, 7235, 7245

Offset: 1

Bernard Schott, Oct 25 2021

When a square ends with 5, it ends with 25.
From  Marius A. Burtea, Oct 25 2021: (Start)
Numbers 75, 765, 7665, 76665, ..., (23*10^k -5) / 3, k >= 1, are terms and have no digits 0, because their squares are 5625, 585225, 58752225, 5877522225, 587775222225, 58777752222225, ...
Also 75, 735, 7335, 73335, ..., (22*10^n+5) / 3, k >= 1, are terms and have no digits 0, because their squares are 5625, 540225, 53802225, 5378022225, 537780222225, 53777802222225, ... (End)

			75^2 = 5625, hence 75 is a term.
235^2 = 55225, hence 235 is not a term.

Cf. A045859, A017330 (squares ending with 5).
Similar to: A348487 (k=1), A348488 (k=4), this sequence (k=5), A348490 (k=6), A348491 (k=9).
Subsequence of A305719.

[n:n in [4..7500]|Intseq(n*n)[1] eq 5 and Intseq(n*n)[#Intseq(n*n)] eq 5 and Intseq(n*n)[-1+#Intseq(n*n)] ne 5 ]; // Marius A. Burtea, Oct 25 2021

Select[5 * Range[2, 1500], (d = IntegerDigits[#^2])[[1]] == d[[-1]] == 5 && d[[2]] != 5 &] (* Amiram Eldar, Oct 25 2021 *)

isok(k) = my(d=digits(sqr(k))); (d[1]==5) && (d[#d]==5) && if (#d>2, (d[2]!=5) && (d[#d-1]!=5), 1); \\ Michel Marcus, Oct 25 2021

from itertools import count, takewhile
def ok(n):
  s = str(n*n); return len(s.rstrip("5")) == len(s.lstrip("5")) == len(s)-1
def aupto(N):
  r = takewhile(lambda x: x<=N, (10*i+5 for i in count(0)))
  return [k for k in r if ok(k)]
print(aupto(7245)) # Michael S. Branicky, Oct 26 2021

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A045788 Squares with initial digit '5'.

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A348489 Positive numbers whose square starts and ends with exactly one 5.

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