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 A139565 Squares without a 0 digit and whose sum of digits minus 1 and product of digits plus 1 are both squares. 1

%I

%S 64,187489,529984,2982529,6165289,45819361,55279225,59613841,85914361,

%T 89151364,114297481,118417924,181252369,183196225,223981156,231861529,

%U 411197284,446519161,582691321,599221441,644195161,876811321,941814721

%N Squares without a 0 digit and whose sum of digits minus 1 and product of digits plus 1 are both squares.

%H Travis Scholl, <a href="/A139565/b139565.txt">Table of n, a(n) for n = 1..122</a>

%H Matthew M. Conroy, <a href="http://www.madandmoonly.com/doctormatt/mathematics/floodProof01.htm">Worst proof ever</a>

%e 64 -> 6+4-1=9 (3) and 6*4+1=25 (5).

%e 187489 -> 1+8+7+4+8+9-1=36 (6) and 1*8*7*4*8*9+1=16129 (127).

%p P:=proc(n) local i,k,w,y; for i from 1 by 1 to n do w:=0; k:=i^2; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; w:=w-1; y:=1; k:=i^2; while k>0 do y:=y*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; y:=y+1; if w=trunc(sqrt(w))^2 and y=trunc(sqrt(y))^2 and y>1 then print(i^2); fi; od; end: P(50000);

%o (PARI) isok(n) = issquare(n) && (d=digits(n)) && vecmin(d) && issquare(vecsum(d)-1) && issquare(prod(k=1, #d, d[k])+1); \\ _Michel Marcus_, Apr 09 2016

%K easy,nonn,base

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 11 2008

%E Name clarified by _Travis Scholl_, Apr 09 2016

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)