Earthworm Sequence/Examples
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Examples of Earthworm Sequence
The earthworm sequence is analysed for all $n \in \set {00, 01, 02, \dotsc, 99}$, not only for the range $\set {10, 11, 12, \dotsc, 99}$.
The first table lists the integers that end up in a loop of $20$ terms:
$n$ $\map h n$ $\map h {\map h n}$ $\map h {\map h {\map h n} }$ $01$, $51$ $02$ $04$ $08$ $27$, $77$ $54$ $08$ $16$ $29$, $79$ $58$ $16$ $32$ $33$, $83$ $66$ $32$ $64$ $41$, $91$ $82$ $64$ $28$ $07$, $57$ $14$ $28$ $56$ $39$, $89$ $78$ $56$ $12$ $03$, $53$ $06$ $12$ $24$ $31$, $81$ $62$ $24$ $48$ $37$, $87$ $74$ $48$ $96$ $49$, $99$ $98$ $96$ $92$ $23$, $73$ $46$ $92$ $84$ $21$, $71$ $42$ $84$ $68$ $17$, $67$ $34$ $68$ $36$ $09$, $59$ $18$ $36$ $72$ $43$, $93$ $86$ $72$ $44$ $11$, $61$ $22$ $44$ $88$ $47$, $97$ $94$ $88$ $76$ $19$, $69$ $38$ $76$ $52$ $13$, $63$ $26$ $52$ $04$
The second table lists the integers that end up in a loop of $4$ terms:
$n$ $\map h n$ $\map h {\map h n}$ $\map h {\map h {\map h n} }$ $05$, $55$ $10$ $20$ $40$ $35$, $85$ $70$ $40$ $80$ $45$, $95$ $90$ $80$ $60$ $15$, $65$ $30$ $60$ $20$
The second table lists the integers that end up in a loop of $1$ term, that is, the degenerate case that ends in $0$:
$25$, $75$ $50$ $00$ $00$