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A080696
Piptorial numbers = product of first n pips or prime-indexed primes.
7
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
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
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