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

Author

Metin Sariyar, Jun 01 2022

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..382
• Michael S. Branicky, Python program
• Kevin Ryde, PARI/GP Code

Crossrefs

Cf. A009994, A034708, A337904.

Programs

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}]

PARI

\\ See links.

Python

# See links.

Extensions

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