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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 4 11:27 EDT 2021. Contains 346447 sequences. (Running on oeis4.)