A276718 Numbers n such that Sum_{k=1..n} d(r(k)) is an integer where d(r(k)) is the decimal fraction 0.r(k), where r(k) is the reverse of k (e.g. d(r(123))=0.321).

4, 52655, 57343, 443749, 526559, 573439, 656249, 2515624, 4437499, 5265599, 5734399, 6562499, 8484374, 44374999, 52655999, 57343999, 65624999, 401953124, 443749999, 526559999, 573439999, 656249999, 698046874, 4437499999, 5265599999, 5734399999, 6562499999, 44374999999, 52655999999, 57343999999, 65624999999

Offset

1,1

Comments

Values of Sum_{k=1..n} d(r(k)) for the terms of the sequence: 1, 26322, 28666, 221869, 263274, 286714, 328119, 1257805, 2218744, 2632794, 2867194, 3281244, 4242180, 22187494, 26327994, 28671994, 32812494, 200976555, 221874994, 263279994, ...

52656*10^j - 1, 57344*10^j - 1, 443750*10^j - 1 and 656250*10^j - 1 are terms for j >= 0 (see comment in A275573). Terms that are not of this form are: 4, 2515624, 8484374, 401953124, 698046874, ... - Chai Wah Wu, Sep 19 2016

Links

Table of n, a(n) for n=1..31.

Formula

A275573(n) = Sum_{k=1..a(n)} d(r(k)) + a(n)*(a(n)+1)/2. - Chai Wah Wu, Sep 19 2016

Example

0.1 + 0.2 + 0.3 + … + 0.35625 + 0.45625 + 0.55625 = 26322.

Maple

with(numtheory): T:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:
P:= proc(q) local a, n; a:=0; for n from 1 to q do a:=a+T(n)/10^(ilog10(n)+1); if type(a, integer) then print(n);
fi; od; end: P(10^9);

Prog

(Python)
from fractions import Fraction
A276718_list, q = [], 0
for i in range(1, 10**6):
    s = str(i)
    q += Fraction(int(s[::-1]), 10**len(s))
    if q.denominator == 1:
        A276718_list.append(i) # Chai Wah Wu, Sep 19 2016

Crossrefs

Cf. A054464, A275573.

Sequence in context: A218405 A259492 A074318 * A102200 A257769 A370683

Adjacent sequences: A276715 A276716 A276717 * A276719 A276720 A276721

Keyword

nonn,base

Author

Paolo P. Lava, Sep 16 2016

Extensions

a(21)-a(27) from Chai Wah Wu, Sep 18 2016

a(28)-a(31) from Chai Wah Wu, Sep 19 2016

Status

approved