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A192280 Characteristic function of numbers that are the product of consecutive primes. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A188318 A189206 A323152 * A266974 A075437 A130047

Adjacent sequences:  A192277 A192278 A192279 * A192281 A192282 A192283

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 26 2011

STATUS

approved

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Last modified May 31 02:51 EDT 2020. Contains 334747 sequences. (Running on oeis4.)