A080696 Piptorial numbers = product of first n pips or prime-indexed primes.

3, 15, 165, 2805, 86955, 3565155, 210344145, 14093057715, 1169723790345, 127499893147605, 16192486429745835, 2542220369470096095, 455057446135147201005, 86915972211813115391955, 18339270136692567347702505, 4419764102942908730796303705

Offset

1,1

Comments

The numbers after the first always end in 5. This is obvious since all pips are odd and their product (excluding 5) = 2k+1 and 5*(2k+1) = 10k+5. Sum of reciprocals converges to 0.4064288978193657814428353009..

Links

Harvey P. Dale, Table of n, a(n) for n = 1..278

Formula

a(n) = Product_{k=1..n} prime(prime(k)). - Michel Marcus, Mar 15 2021

Example

prime(prime(1)), prime(prime(1))*prime(prime(2)), ...
pip(1) = 3, pip(2) = 5, pip(3) = 11; piptorial(3) = 3*5*11 = 165.

Mathematica

nn=50; FoldList[Times, 1, Transpose[Select[Thread[{Prime[Range[nn]], Range[nn]}], PrimeQ[ Last[#]]&]][[1]]] (* Harvey P. Dale, Jul 05 2011 *)
FoldList[Times, Table[Prime[Prime[n]], {n, 20}]] (* Harvey P. Dale, May 06 2018 *)

Prog

(PARI) piptorial(n) = {sr=0; pr=1; for(x=1, n, y=prime(prime(x)); pr*=y; print1(pr" "); sr+=1.0/pr; ); print(); print(sr) }
(PARI) a(n) = prod(k=1, n, prime(prime(k))); \\ Michel Marcus, Mar 15 2021
(Python)
from sympy import prime, nextprime
def aupton(terms):
  prod, p, alst = 1, 2, []
  while len(alst) < terms:
    p, prod = nextprime(p), prod * prime(p)
    alst.append(prod)
  return alst
print(aupton(16)) # Michael S. Branicky, Mar 15 2021

Crossrefs

Cf. A006450.

Sequence in context: A329557 A108975 A097489 * A015013 A269694 A153280

Adjacent sequences: A080693 A080694 A080695 * A080697 A080698 A080699

Keyword

easy,nonn

Author

Cino Hilliard, Mar 04 2003

Extensions

Name clarified by Michel Marcus, Aug 04 2015

More terms from Harvey P. Dale, May 06 2018

Status

approved