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%I #9 Oct 09 2017 20:47:18
%S 0,65340,659340,6599340,65999340,653465340,659999340,6534065340,
%T 6599999340,65340065340,65934659340,65999999340,653400065340,
%U 659340659340,659999999340,6534000065340,6534653465340,6593400659340,6599346599340,6599999999340
%N Numbers n such that n = 15*reversal(n).
%C 30 divides all terms of the sequence. For all nonnegative integers m and n all numbers of the form f1(m,n) = 660(10^(m + 2) - 1)*(10^((m + 4)*n) - 1)/(10^(m + 4) - 1) are in the sequence, in fact f1(m,n) = (65.(9)(m).34)(n).0 where dot between numbers means concatenation and "(r)(t)" means number of r's is t. With this definition a(1) = 0 = f1(0,0), a(2) = 65340 = f1(0,1), a(3) = 659340 = f1(1,1), a(4) = 6599340 = f1(2,1), a(5) = 65999340 = f1(3,1), a(6) = 653465340 = f1(0,2), a(7) = 659999340 = f1(4,1), a(9) = 6599999340 = f1(5,1), etc. f1(m,1) = 660(10^(m + 2) - 1) = 65.(9)(m).340, f1(m,2) = 65.(9)(m).34.65.(9)(m).340, etc. Let g(s,t,r) = s*(10^((L+t)*(1+r))-1)/(10^(L+t)-1) where L = number of digits of s, in fact g(s,t,r) = (s.(0)(t))(r).s so the function g is the same function that has been defined in the sequence A101704. If s is in the sequence then all numbers of the form g(s,t,r) for nonnegative integers t and r are in the sequence. Next term is greater than 11*10^9. It seems that the eleven next terms are 65340065340, 65934659340, 65999999340, 653400065340, 659340659340 659999999340, 6534000065340, 6534653465340, 6593400659340, 6599346599340 and 6599999999340. Is it true that, all terms of this sequence are of the form g(f1(m,n),r,t)?
%H Ray Chandler, <a href="/A102277/b102277.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 10*A101704(n) = 20*A101706(n). - _Ray Chandler_, Oct 09 2017
%e g(65340,0,2)= (65340)(3) = 653406534065340 is in the sequence because reversal(653406534065340) = 43560435604356 = (1/15)*653406534065340.
%t Do[If[n == 15*FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 0, 11000000000, 30}]
%Y Cf. A001232, A008918, A101704, A101705, A101706.
%K base,nonn
%O 1,2
%A _Farideh Firoozbakht_, Jan 04 2005
%E More terms from _Ray Chandler_, Oct 09 2017
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