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, 13, 145, 153, 1825, 15789, 16666, 21583, 216666, 2416666, 28428571, 265833333, 3194444444, 3333333333, 9111111111, 35333333333, 3166666666666, 3819444444444, 26666666666666, 34166666666666, 527857142857142, 3944444444444444, 6135714285714285, 615833333333333333

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