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A343496
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First point of the straight lines in A340649.
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1
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5, 31, 194, 1061, 6456, 40080, 251721, 1617206, 10553419, 69709769, 465769825
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OFFSET
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1,1
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COMMENTS
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prime(a(n)+1) - prime(a(n)) = n*2. E.g., for n=4: prime(a(4)+1) - prime(a(4)) = 4*2, prime(1062) - prime(1061) = 4*2, 8521 - 8513 = 8.
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LINKS
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FORMULA
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EXAMPLE
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For n=1, consider k's with prime gap 1*2 = 2, i.e., k's such that A001223(k)=2. k=5 is the first place where A001223(k)=2 and A141042(k)=A340649(k), so a(1)=5.
For n=2, consider k's with prime gap 2*2 = 4, i.e., k's such that A001223(k)=4. k=31 is the first place where A001223(k)=4 and A141042(k)=A340649(k), so a(2)=31.
For n=3, consider k's with prime gap 3*2 = 6, i.e., k's such that A001223(k)=6. k=194 is the first place where A001223(k)=6 and A141042(k)=A340649(k), so a(3)=194.
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PROG
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(Ruby) n = 1
last_prime = 2
find_gap = 2
result = []
Prime.each(10_000) do |prime|
next if prime == 2
gap = prime - last_prime
if gap == find_gap
value = (n * prime) % last_prime
if value == n * gap
result << n
find_gap += 2
end
end
n += 1
last_prime = prime
end
p result
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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