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

1,1

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

Formula

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

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 *)

Prog

(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]))));

Crossrefs

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

Sequence in context: A323514 A369660 A353495 * A044940 A284261 A037825

Adjacent sequences: A302044 A302045 A302046 * A302048 A302049 A302050

Keyword

nonn

Author

Antti Karttunen, Apr 24 2018

Status

approved