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A102277 Numbers n such that n = 15*reversal(n). 1
0, 65340, 659340, 6599340, 65999340, 653465340, 659999340, 6534065340, 6599999340, 65340065340, 65934659340, 65999999340, 653400065340, 659340659340, 659999999340, 6534000065340, 6534653465340, 6593400659340, 6599346599340, 6599999999340 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)?

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 10*A101704(n) = 20*A101706(n). - Ray Chandler, Oct 09 2017

EXAMPLE

g(65340,0,2)= (65340)(3) = 653406534065340 is in the sequence because reversal(653406534065340) = 43560435604356 = (1/15)*653406534065340.

MATHEMATICA

Do[If[n == 15*FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 0, 11000000000, 30}]

CROSSREFS

Cf. A001232, A008918, A101704, A101705, A101706.

Sequence in context: A015344 A184148 A083608 * A013692 A037164 A288990

Adjacent sequences:  A102274 A102275 A102276 * A102278 A102279 A102280

KEYWORD

base,nonn

AUTHOR

Farideh Firoozbakht, Jan 04 2005

EXTENSIONS

More terms from Ray Chandler, Oct 09 2017

STATUS

approved

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Last modified April 22 14:18 EDT 2019. Contains 322349 sequences. (Running on oeis4.)