login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102863 a(n)=1 if at least one of the first n primes is a divisor of the sum of the first n primes; otherwise a(n)=0. 3
1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = 0 if and only if n is in A013916. - Robert Israel, Jan 04 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(2)=0 because none of the first 2 primes (2, 3) is a divisor of 2+3; a(5)=1 because among the first 5 primes (namely, 2,3,5,7,11) there are divisors of 2+3+5+7+11=28.

MAPLE

with(numtheory):

a:=proc(n)

   if nops(factorset(sum(ithprime(k), k=1..n)) intersect {seq(ithprime(j), j=1..n)}) >0 then

      1

   else

      0

   fi

end:

seq(a(n), n=1..130); # Emeric Deutsch

# alternative:

N:= 500: # to get the first N terms

A:= Vector(N):

S:= 2: P:= 2: p:= 2: A[1]:= 1:

for n from 2 to N do

  p:= nextprime(p);

  S:= S+p; P:= P*p;

  if igcd(S, P) > 1 then A[n]:= 1 fi

od:

convert(A, list); # Robert Israel, Jan 04 2017

MATHEMATICA

a[n_] := Module[{pp = Prime[Range[n]], t}, t = Total[pp]; Boole[AnyTrue[pp, Divisible[t, #]&]]];

Array[a, 100] (* Jean-Fran├žois Alcover, Jun 16 2020 *)

CROSSREFS

A105783(n) gives number of primes among the first n primes that are divisors of the sum of the first n primes.

Cf. A013916, A136443.

Sequence in context: A195062 A229940 A179761 * A131483 A077052 A133566

Adjacent sequences:  A102860 A102861 A102862 * A102864 A102865 A102866

KEYWORD

easy,nonn

AUTHOR

Giovanni Teofilatto, Mar 01 2005

EXTENSIONS

Edited and extended by Emeric Deutsch, Apr 19 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 04:42 EDT 2021. Contains 343146 sequences. (Running on oeis4.)