cp's OEIS Frontend

A225885 Square numbers that remain square when their most-significant (or leftmost) digit is removed.

%I A225885 #39 Feb 13 2018 19:20:12
%S A225885 1,4,9,49,64,81,100,225,400,625,900,1225,2025,3025,4225,4900,5625,
%T A225885 6400,7225,8100,9025,10000,15625,22500,27225,30625,34225,40000,42025,
%U A225885 50625,60025,62500,70225,75625,81225,90000,93025,105625,122500,202500,275625,302500,330625
%N A225885 Square numbers that remain square when their most-significant (or leftmost) digit is removed.
%C A225885 The first three are the only terms not divisible by 25 (and thus, not ending in 00 or 25). If 100 is a term, then the sequence should start with 3 more initial terms, namely (1, 4, 9, ...) - _M. F. Hasler_, Nov 01 2014
%H A225885 Chai Wah Wu, <a href="/A225885/b225885.txt">Table of n, a(n) for n = 1..3000</a> (n = 4..403 from Christian N. K. Anderson and Kevin L. Schwartz)
%e A225885 225 = 15^2 becomes 25 = 5^2, 105625 = 325^2 becomes 5625 = 75^2.
%t A225885 b^2 /. Flatten[Outer[Solve[a^2 + #2*10^#1 == b^2 && 0 <= a < Sqrt[10^#1] && Sqrt[#2*10^#1] <= b < Sqrt[10^(#1 + 1)], {a, b}, Integers] &, Range[0, 5], Range[9]], 2] (* _Davin Park_, Dec 30 2016 *)
%o A225885 (R)
%o A225885 no0<-function(s){ while(substr(s,1,1)=="0" & nchar(s)>1) s=substr(s,2,nchar(s)); s};
%o A225885 issquare<-function(x) ifelse(as.bigz(x)<2,T,all(table(as.numeric(gmp::factorize(x)))%%2==0));
%o A225885 which(sapply(1:200,function(x) issquare(no0(substr(x^2,2,ndig(x^2)))))>0)^2
%o A225885 (PARI) is_A225885(n)=issquare(n%10^(#Str(n)-1))&&issquare(n)&&n>9 \\ _M. F. Hasler_, Nov 01 2014
%Y A225885 Cf. A225873, A249587, A247267.
%K A225885 nonn,base
%O A225885 1,2
%A A225885 _Kevin L. Schwartz_ and _Christian N. K. Anderson_, May 19 2013
%E A225885 1,4,9 added (per _M. F. Hasler_'s comment) by _Chai Wah Wu_, Nov 03 2014