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A354466 Numbers k such that the decimal expansion of the sum of the reciprocals of the digits of k starts with the digits of k in the same order. 1
1, 13, 145, 153, 1825, 15789, 16666, 21583, 216666, 2416666, 28428571, 265833333, 3194444444, 3333333333, 9111111111, 35333333333, 3166666666666, 3819444444444, 26666666666666, 34166666666666, 527857142857142, 3944444444444444, 6135714285714285, 615833333333333333 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is infinite because all numbers of the form 10^(10^n-6) + 6*(10^(10^n-6)-1)/9, (n>0) are terms.

All terms are zeroless since 1/0 is undefined.

If n gives a sum < 1 then that sum is taken as 0.xyz.. but n does not start with 0, so not a term.

LINKS

Kevin Ryde, Table of n, a(n) for n = 1..382

Michael S. Branicky, Python program

Kevin Ryde, PARI/GP Code

EXAMPLE

28428571 is a term because 1/2 + 1/8 + 1/4 + 1/2 + 1/8 + 1/5 + 1/7 + 1/1 = 2.8428571...

825 is not a term since 1/8 + 1/2 + 1/5 = 0.825.

MATHEMATICA

Do[If[FreeQ[IntegerDigits[n], 0]&&Floor[Total[1/IntegerDigits[n]]*10^(IntegerLength[n]-IntegerLength[Floor[Total[1/IntegerDigits[n]]]])]==n&&Floor[Total[1/IntegerDigits[n]]]>0, Print[n]], {n, 1, 216666}]

PROG

(Python) See links.

(PARI) See links.

CROSSREFS

Cf. A009994, A034708, A337904.

Sequence in context: A134489 A064525 A065411 * A038492 A270579 A297223

Adjacent sequences: A354463 A354464 A354465 * A354467 A354468 A354469

KEYWORD

nonn,base

AUTHOR

Metin Sariyar, Jun 01 2022

EXTENSIONS

a(12)-a(24) from Michael S. Branicky, Jun 03 2022

STATUS

approved

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Last modified February 5 00:04 EST 2023. Contains 360082 sequences. (Running on oeis4.)