Recreational Mathematics · Pattern Families

Patterned Single-Letter
Representations Generator

Search, extend and verify patterned identities constructed from one repeated letter a.

Created by Inder J. Taneja
Verified-rule edition. The source contains 1,455 written families. This generator uses 1,325 distinct rules inferred from fully exact families; every displayed extension is checked independently for a = 1,…,9.

Results

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Enter a target or explore an authored family.

Collection summary

1,455written families
5,827source rows
1,325distinct verified rules
1–9exact substitutions checked

How extension works

Within each four-row family, the generator identifies the fixed operator structure and the arithmetic growth of every repeated a-block. It then extends those block lengths, calculates the resulting target, and accepts the new row only when the identity remains exact for all nine possible digits.

Source status: the first four rows are marked “author’s row”; later rows are marked “generated extension.” Duplicate families and rows containing transcription or identity errors are excluded.

Individual fallback: if no pattern family contains the requested target, the generator checks the author’s running-type or fraction-type collection and then the structural single-value constructor. An isolated identity is labelled as an individual representation and is never presented as a pattern.