第 20438 題：子數列

原題與已知條件

自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={"outer_start":0,"outer_step":3,"inner_start":0,"inner_step":1,"j":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={"outer_start":0,"outer_step":3,"inner_start":0,"inner_step":1,"j":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-subsequence

逐步推導

source operation=subseq-composed-index;original snapshot and mathematics retained

explicit ordered source output fields=[j, inner_index, source_index, composed_step, strictly_increasing, certificate]

outer index k:ORIGINAL nonnegative start=0;positive integer step=3;F(q)=start+step*q for EVERY natural q>=0

F(q)>=start>=0 and for ANY q<r,F(r)-F(q)=(3)*(r-q)>0;strictly increasing on ALL naturals,not just the evaluated prefix

inner index l:ORIGINAL nonnegative start=0;positive integer step=1;F(q)=start+step*q for EVERY natural q>=0

F(q)>=start>=0 and for ANY q<r,F(r)-F(q)=(1)*(r-q)>0;strictly increasing on ALL naturals,not just the evaluated prefix

subsequence inner step times ORIGINAL j := mul(1, 13)

subsequence inner step times ORIGINAL j = 13

subsequence ORIGINAL inner index l(j) := sum(0, 13)

subsequence ORIGINAL inner index l(j) = 13

subsequence outer step times INNER result := mul(3, 13)

subsequence outer step times INNER result = 39

subsequence ORIGINAL composed index k(l(j)) := sum(0, 39)

subsequence ORIGINAL composed index k(l(j)) = 39

subsequence composed positive step := mul(3, 1)

subsequence composed positive step = 3

ORIGINAL outer k(i)=0+3i;inner l(j)=0+1j;actual j=13;inner value=13

outer(inner(j))=39;for EVERY j,composed consecutive difference=3>0;exact evaluated fields within SAFE integer range

逐步反向核對

• S009 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S008 · premise_and_result_audit — 以精確有理數重算 subsequence composed positive step，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 subsequence ORIGINAL composed index k(l(j))，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 subsequence outer step times INNER result，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 subsequence ORIGINAL inner index l(j)，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 subsequence inner step times ORIGINAL j，不以小數近似替代。
• S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

(13, 13, 39, 3, 是, composition_remains_strictly_increasing)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。