Inverse prime-return dynamics of the Rowland auxiliary recurrence

We invert the dynamics of the Rowland auxiliary recurrence T(x)=x+lpf(x)-1 on primes. Exact predecessor rule, counting recursion W(z)=|Phi^{-1}(z)|, generation profiles W_k, basin size A# and depth D, complete fan-in sweeps up to 10^6 (record W(597407)=31). All quantities machine-checked and cross-validated by exhaustive forward simulation.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-25
DOI
https://doi.org/10.5281/zenodo.22079593
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Inverse prime-return dynamics of the Rowland auxiliary recurrence

L Stankusch
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Inverse prime-return dynamics of the Rowland auxiliary recurrence

L Stankusch
preprint en

Abstract

We invert the dynamics of the Rowland auxiliary recurrence T(x)=x+lpf(x)-1 on primes. Exact predecessor rule, counting recursion W(z)=|Phi^{-1}(z)|, generation profiles W_k, basin size A# and depth D, complete fan-in sweeps up to 10^6 (record W(597407)=31). All quantities machine-checked and cross-validated by exhaustive forward simulation.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Inverse prime-return dynamics of the Rowland auxiliary recurrence — L Stankusch · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS