A192280 Characteristic function of numbers that are the product of consecutive primes.

1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0

Offset

1

Comments

More exactly: characteristic function of squarefree numbers with no gaps in their prime factorization. - Antti Karttunen, Dec 15 2017

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for characteristic functions

Formula

a(A073485(n)) = 1, a(A193166(n)) = 0.

Mathematica

Array[Boole[Or[# == 1, PrimeQ[#], Union@ Differences@ PrimePi@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger[#] ] == {1} ] ] &, 105] (* Michael De Vlieger, Dec 16 2017 *)

Prog

(Haskell)
a192280 n = fromEnum $ a053590 n == n
a192280_list = map a192280 [1..]
-- Reinhard Zumkeller, May 28 2012, Aug 26 2011
(PARI) A192280(n) = { if(1==n, return(1)); if(!issquarefree(n), return(0)); my(ps=factor(n)[, 1], pis=vector(length(ps), i, primepi(ps[i])), diffsminusones = vector(length(pis)-1, i, (pis[i+1]-pis[i])-1)); !vecsum(diffsminusones); }; \\ Antti Karttunen, Dec 15 2017

Crossrefs

Cf. A000040, A001221, A020639, A053590, A296210.

Characteristic function of A073485.

Sequence in context: A361897 A189206 A323152 * A342005 A354355 A266974

Adjacent sequences: A192277 A192278 A192279 * A192281 A192282 A192283

Keyword

nonn

Author

Reinhard Zumkeller, Aug 26 2011

Status

approved