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Investigate test-pari failure for A131083 periodic sequence #637

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Investigate test-pari failure for A131083 periodic sequence #637

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0ca8d98
Initial plan
Copilot Dec 13, 2025
c7eda0a
Initial exploration of A131083 test-pari failure
Copilot Dec 13, 2025
6fb3208
Fix calculation of initial terms needed for formula generation
Copilot Dec 13, 2025
6e1c755
Attempted fix for initial terms calculation - partial progress
Copilot Dec 13, 2025
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16 changes: 16 additions & 0 deletions pari-result-279.txt
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Original file line number Diff line number Diff line change
@@ -0,0 +1,16 @@
26
16
6
2
6
16
26
 *** [...] at: ...,6,if(n==2,16,if(n==1,26,a(n-8))))))))
 *** ^-------------
 *** in function a: ...,6,if(n==2,16,if(n==1,26,a(n-8))))))))
 *** ^-------------
 *** in function a: ...,6,if(n==2,16,if(n==1,26,a(n-8))))))))
 *** ^-------------
*** deep recursion.
*** Break loop: type 'break' to go back to GP prompt
[?2004hbreak> [?2004l[?2004h
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16 changes: 16 additions & 0 deletions pari-result-745.txt
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Original file line number Diff line number Diff line change
@@ -0,0 +1,16 @@
26
16
6
2
6
16
26
 *** [...] at: ...,6,if(n==2,16,if(n==1,26,a(n-8))))))))
 *** ^-------------
 *** in function a: ...,6,if(n==2,16,if(n==1,26,a(n-8))))))))
 *** ^-------------
 *** in function a: ...,6,if(n==2,16,if(n==1,26,a(n-8))))))))
 *** ^-------------
*** deep recursion.
*** Break loop: type 'break' to go back to GP prompt
[?2004hbreak> [?2004l
7 changes: 7 additions & 0 deletions src/form/formula_gen.cpp
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Expand Up @@ -458,6 +458,13 @@ int64_t getNumInitialTermsNeeded(int64_t cell, const std::string& fname,
int64_t terms_needed = 0;
if (stateful.find(cell) != stateful.end()) {
terms_needed = (ie.getLoopCounterDecrement() * stateful.size());
// For the counter cell (main function in periodic sequences), add one
// additional initial term to complete the recurrence period. This ensures
// that for a recurrence a(n) = a(n-k), we have k initial terms to avoid
// deep recursion in PARI evaluation.
if (cell == ie.getSimpleLoop().counter) {
terms_needed += ie.getLoopCounterDecrement();
}
}
return terms_needed;
}
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19 changes: 19 additions & 0 deletions tests/programs/oeis/131/A131083.asm
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; A131083: Periodic sequence (26, 16, 6, 2, 6, 16, 26, 30).
; Submitted by loader3229
; 26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30,26,16,6,2,6,16,26,30
; Formula: a(n) = a(n-8), a(7) = 26, a(6) = 16, a(5) = 6, a(4) = 2, a(3) = 6, a(2) = 16, a(1) = 26

#offset 1

mov $2,26
mov $3,16
mov $4,6
mov $5,2
sub $0,1
lpb $0
mul $2,-1
rol $2,4
add $5,32
sub $0,1
lpe
mov $0,$2