A302047 a(n) = 1 if n = prime(k)*prime(2+k) for some k, otherwise 0.

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

Offset: 1

Author

Antti Karttunen, Apr 24 2018

Keywords

• nonn

Comments

Characteristic function for prime(n)*prime(n+2) (A090076).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..66013
• Index entries for characteristic functions
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A090076, A246277, A280710, A302048, A302049.

Programs

Mathematica

Array[Boole@ And[Length@ # == 2, Max@ #[[All, -1]] == 1, Subtract @@ PrimePi[#[[All, 1]]] == -2 ] &@ FactorInteger@ # &, 120] (* or *)
With[{s = Array[Prime[#] Prime[# + 2] &, 5]}, ReplacePart[ConstantArray[0, Max@ s], Map[# -> 1 &, s] ] ] (* Michael De Vlieger, Apr 27 2018 *)
Module[{pp2=Table[Prime[n]Prime[n+2],{n,5}],nn},nn=Max[pp2];Table[ If[ MemberQ[ pp2,k],1,0],{k,nn}]] (* Harvey P. Dale, Dec 13 2021 *)

PARI

A302047(n) = if((2!=bigomega(n))||(2!=omega(n)),0,my(f=factor(n)); (f[2,1] == nextprime(1+nextprime(1+f[1,1]))));

Formula

a(n) = A185015(A246277(n)).