A343496 - OEIS

A343496

First point of the straight lines in A340649.

5, 31, 194, 1061, 6456, 40080, 251721, 1617206, 10553419, 69709769, 465769825

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OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..11.

Simon Strandgaard, Visualization of the first 5 terms.

FORMULA

a(n) = smallest k that satisfies A001223(k) = 2*n and A340649(k) = A141042(k).

EXAMPLE

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.

PROG

(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

n += 1

last_prime = prime

end

p result

CROSSREFS

Cf. A000040, A001223, A141042, A340649, A029707, A029709, A320701, A320702, A320703.

Sequence in context: A015540 A014987 A365741 * A108079 A164038 A260782

Adjacent sequences: A343493 A343494 A343495 * A343497 A343498 A343499

KEYWORD

nonn,more

AUTHOR

Simon Strandgaard and Jamie Morken, Apr 17 2021

STATUS

approved