A342027 a(n) is the least m such that A341284(m) = 2*n*prime(m+1) - prime(m).

2, 3, 6, 16, 24, 42, 23, 50, 47, 133, 138, 67, 161, 106, 30, 675, 455, 338, 697, 137, 488, 692, 189, 934, 1863, 1552, 518, 450, 2036, 1815, 2856, 3635, 6784, 8781, 2787, 2790, 99, 11396, 3903, 2539, 9722, 1851, 6399, 7388, 6592, 24371, 12408, 14059, 32846, 21934, 13490, 72170, 42106, 15469, 45948

Offset

1,1

Comments

a(n) is the least m such that 2*n*prime(m+1)-prime(m) is prime while for all j < n, 2*j*prime(m+1)-prime(m) is not prime.

Links

Robert Israel, Table of n, a(n) for n = 1..175

Formula

A341284(a(n)) = 2*n*prime(a(n)+1)-prime(a(n)).

Example

For k=4, A341284(16) = 419 = 2*4*prime(17)-prime(16) and a(4) = 16.

Maple

N:= 60: # for a(1) to a(N)
V:= Vector(N): count:= 0:
g:= proc(n) local k, pn, p1;
  pn:= ithprime(n); p1:= ithprime(n+1);
  for k from 2*p1-pn by 2*p1 to 2*N*p1-pn do
    if isprime(k) then return (k+pn)/(2*p1) fi
od;
N+1
end proc:
for n from 2 while count < N do
  v:= g(n);
    if v <= N and V[v] = 0 then V[v]:= n; count:= count+1 fi
od:
convert(V, list);

Crossrefs

Cf. A341284.

Sequence in context: A109162 A215659 A028688 * A343197 A030753 A003040

Adjacent sequences: A342024 A342025 A342026 * A342028 A342029 A342030

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 25 2021

Status

approved