The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A242268 Squares not ending in 00 that remain squares if prefixed with the digit 1. 4
 225, 5625, 5405625, 23765625, 2127515625, 58503515625, 51921031640625, 250727431640625, 20090404775390625, 608180644775390625, 498431438615478515625, 2642208974615478515625, 189450791534674072265625, 6319494849134674072265625, 9981411957966851806640625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It can easily be shown that all squares that remain squares if prefixed with the digit 1 end in 00 or 25 and, moreover, that all squares ending in 00 are multiples of the squares ending in 5 (factor: 10^(2*n)). Subsequence of A167035. - Michel Marcus, Sep 08 2014 LINKS Reiner Moewald, Table of n, a(n) for n = 1..102 EXAMPLE 225 = 15*15 and 1225 = 35*35. MAPLE A:= {}: for m from 3 to 100 do   cand1:= floor(log[5](1/2*(1+sqrt(2))*10^(m/2)));   cand2:= floor(log[5](2*(1+sqrt(2))*(5/2)^(m/2)));   s1:= 5^cand1 - 10^m/4/5^cand1;   s2:=  2^m/4*5^cand2 - 5^(m-cand2);   if s1^2 >= 10^(m-1) then A:= A union {s1^2} fi;   if s2^2 >= 10^(m-1) then A:= A union {s2^2} fi; od: A; # Robert Israel, Sep 08 2014 PROG (Python) import math def power(a, n): ...pow = 1 ...for i in range(0, n): ......pow = pow * a ...return pow end = 50 for n in range(1, end): ...l1 = 1/math.log(5)*(math.log(math.sqrt(2)-1)+(n-2)/2*math.log(2))+ n/2 ...u1 = 1/math.log(5)*(math.log(math.sqrt(11)-1)+(n-3)/2*math.log(2))+ (n-1)/2 ...if math.ceil(l1) == math.floor(u1) and math.ceil(l1)>0: ......p = math.ceil(l1) ......x = power(5, p)*(-1)+power(2, n-2)*power(5, n-p) ......print(x*x) ...l2 = 1/math.log(5)*(math.log(math.sqrt(11)+1)+(n-3)/2*math.log(2))+ (n-1)/2 ...u2 = 1/math.log(5)*(math.log(math.sqrt(2)+1)+(n-2)/2*math.log(2))+ n/2 ...if math.ceil(l2) == math.floor(u2) and math.ceil(l2)>0: ......p = math.ceil(l2) ......x = power(5, p)-power(2, n-2)*power(5, n-p) ......print(x*x) print('End.') (PARI) for(n=1, 10^20, p=n^2; if(p%100, s=concat("1", Str(p)); if(issquare(eval(s)), print1(p, ", ")))) \\ Derek Orr, Aug 23 2014 CROSSREFS Cf. A167035. Sequence in context: A297760 A167035 A167042 * A164763 A164752 A151651 Adjacent sequences:  A242265 A242266 A242267 * A242269 A242270 A242271 KEYWORD nonn,base AUTHOR Reiner Moewald, Aug 16 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 06:59 EDT 2022. Contains 354074 sequences. (Running on oeis4.)