Patterns in Reversible Semi-Selfie Numbers

A power N=a^k is a semi-selfie number when its digits, in the same order, can be split into groups with plus or minus signs adding up to the base a. This work studies 121 patterns of semi-selfie numbers with first bases from 1 to 2500, and asks which of them still work when the digits of N are read backwards. Of the 121 patterns, 45 are reversible in every line, and 35 of these have a regular reverse pattern. The other 76 are not reversible: 18 reverse only in some lines, 17 fail already in the first line, and 41 end in 0. The work also lists the semi-selfie powers with single-digit bases below 10^11: 94 of the 98 are reversible.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24121861
Primary Topic
Smarandache Functions and Recreational Number Theory
Type
preprint
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preprint

Patterns in Reversible Semi-Selfie Numbers

Inder Jeet Taneja
Zenodo (CERN European Organization for Nuclear Research)
Smarandache Functions and Recreational Number Theory
preprint

Patterns in Reversible Semi-Selfie Numbers

Inder Jeet Taneja
preprint en

Abstract

A power N=a^k is a semi-selfie number when its digits, in the same order, can be split into groups with plus or minus signs adding up to the base a. This work studies 121 patterns of semi-selfie numbers with first bases from 1 to 2500, and asks which of them still work when the digits of N are read backwards. Of the 121 patterns, 45 are reversible in every line, and 35 of these have a regular reverse pattern. The other 76 are not reversible: 18 reverse only in some lines, 17 fail already in the first line, and 41 end in 0. The work also lists the semi-selfie powers with single-digit bases below 10^11: 94 of the 98 are reversible.

Zenodo (CERN European Organization for Nuclear Research)
Universidade Federal de Santa Catarina (BR)
Smarandache Functions and Recreational Number Theory
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