Question 7193: Finite Sequence Query Bounds before Evaluation

Original question and givens

N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=5+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

• G001 — N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. L=4; only 0≤n<L is allowed for a_n=5+(1)n. Ordered candidate indices=[0, 3, 4]. Give (L, index-eligibility mask, legal term values or invalid-index).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-sequence

Step-by-step derivation

N starts at0;ordered finite indices and repeated values retained

given recurrences differ from guessing an infinite rule from observations

query0 d times index := mul(1, 0)

query0 d times index = 0

query0 legal sequence value := sum(5, 0)

query0 legal sequence value = 5

candidate index=0;0≤index<4=Yes

value/status=5

query1 d times index := mul(1, 3)

query1 d times index = 3

query1 legal sequence value := sum(5, 3)

query1 legal sequence value = 8

candidate index=3;0≤index<4=Yes

value/status=8

candidate index=4;0≤index<4=No

value/status=invalid index

Reverse checks

• S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S006 · premise_and_result_audit — Recompute query1 legal sequence value with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute query1 d times index with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S003 · premise_and_result_audit — Recompute query0 legal sequence value with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute query0 d times index with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(4, [Yes, Yes, No], [5, 8, invalid-index])

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.