A294299 a(n) = (prime(n+A105342(n)) - A105342(n))/prime(n).

1, 3, 2, 2, 3, 2, 12, 7, 2, 2, 2, 3, 10, 2, 2, 14, 5, 2, 2, 4, 2, 4, 10, 14, 5, 9, 2, 9, 4, 8, 7, 5, 19, 2, 3, 9, 4, 6, 18, 31, 3, 3, 2, 11, 2, 3, 9, 10, 4, 8, 13, 5, 3, 38, 10, 3, 8, 3, 19, 9, 2, 3, 2, 16, 3, 4, 9, 8, 22, 5, 10, 4, 3, 3, 2, 7, 3, 4, 10, 11, 7, 9, 34, 18, 5, 9, 3, 7, 25, 10, 2, 9, 14

Offset

1,2

Comments

If p = prime(n), a(n) is the least m such that there is some prime q with m*p <= q < (m+1)*p and A000720(q) = n + q - m*p.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 2 because A105342(3) = 3, prime(3+3) = 13, prime(3) = 5, and (13-3)/5 = 2.  Thus with p=5 and q = 13, 2*p <= q < 3*p and A000720(q) = 6 = 3 + 13 - 2*5.

Maple

f:= proc(n) local p, k;
  p:= ithprime(n);
  for k from 1 do
      if ithprime(n+k) - k mod p = 0 then return (ithprime(n+k)-k)/p fi
  od:
end proc:
map(f, [$1..150]);

Crossrefs

Cf. A000720, A105342.

Sequence in context: A049234 A299351 A358935 * A125504 A243929 A350285

Adjacent sequences: A294296 A294297 A294298 * A294300 A294301 A294302

Keyword

nonn

Author

Robert Israel, Oct 29 2017

Status

approved