A214362 Arithmetic mean of next a(n) successive positive integers is prime.

3, 3, 1, 7, 5, 7, 5, 11, 1, 7, 5, 7, 9, 3, 9, 11, 5, 3, 1, 7, 5, 23, 1, 19, 9, 11, 1, 3, 17, 23, 1, 7, 5, 7, 17, 7, 5, 11, 1, 19, 9, 3, 5, 23, 9, 3, 9, 7, 5, 7, 1, 11, 5, 3, 13, 7, 17, 7, 5, 11, 1, 7, 17, 7, 9, 11, 13, 27, 5, 7, 5, 11, 9, 3, 9, 7, 5, 3, 1, 23, 1

Offset: 1

Author

Alex Ratushnyak, Jul 18 2012

Keywords

• nonn
• easy

Comments

Corresponding primes: A062044(n).

All terms are odd. - Robert Israel, Jan 17 2017

Examples

			(1+2+3)/3 = 2 is prime, so a(1)=3,
then (4+5+6)/3 = 5 is prime, so a(2)=3,
then 7/1 = 7 is prime, so a(3)=1,
then (8+9+10+11+12+13+14)/7 = 11 is prime, so a(4)=7.
		

Links

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

Crossrefs

Cf. A000040, A062042, A062044, A213815.

Programs

Maple

t:= 1:
for n from 1 to 100 do
  for s from 1 by 2 do
    if isprime((2*t + s - 1)/2) then
      A[n]:= s; t:= t+s; break
    fi
od od:
seq(A[n],n=1..100); # Robert Israel, Jan 17 2017

PARI

firstTerms(n)={
my(k=1,j=1,x,y,a=vector(n));
while(j<=n,x=0;while(!isprime(k+x),x++);y=2*x+1;k+=y;a[j]=y;j++);
return(a)} \\ R. J. Cano, Jan 17 2017

Formula

a(n) = 2*(A062042(n)-A062042(n-1))+(-1)^n for n >= 2. - Robert Israel, Jan 17 2017