A173631 a(n) = ceiling(sqrt(4*P_n)), where P_n is product of first n primes.

2, 3, 5, 11, 29, 97, 347, 1429, 6229, 29873, 160869, 895680, 5448207, 34885543, 228759799, 1568298164, 11417382972, 87698582661, 684947826800, 5606539592683, 47241542317190, 403631914492643, 3587558929043911, 32684217334320604, 308342289648017960, 3036819365023555974

Offset: 0

Author

Vladimir Shevelev, Nov 23 2010

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..632

Crossrefs

Cf. A000040, A002110.

Programs

Maple

P:= 1: p:= 1: A[0]:= 2:
for n from 1 to 30 do
  p:= nextprime(p);
  P:= P*p;
  A[n]:= ceil(sqrt(4*P));
od:
seq(A[i],i=0..30); # Robert Israel, Mar 18 2020

Mathematica

p=4; Join[{Sqrt[p]}, Table[p=p*Prime[n]; Ceiling[Sqrt[p]], {n, 25}]]

PARI

a(n) = sqrtint(4*prod(k=1, n, prime(k)) - 1) + 1; \\ Michel Marcus, Feb 22 2016; corrected Jun 16 2022

Formula

a(n) = ceiling(sqrt(4*A002110(n))). - Michel Marcus, Feb 22 2016

Extensions

Extended by T. D. Noe, Nov 23 2010