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A214362 Arithmetic mean of next a(n) successive positive integers is prime. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Corresponding primes: A062044(n).

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

LINKS

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

FORMULA

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

EXAMPLE

(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.

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

PROG

(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

CROSSREFS

Cf. A000040, A062042, A062044, A213815.

Sequence in context: A322148 A084144 A306759 * A180735 A344726 A116401

Adjacent sequences:  A214359 A214360 A214361 * A214363 A214364 A214365

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Jul 18 2012

STATUS

approved

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Last modified September 25 23:09 EDT 2021. Contains 347664 sequences. (Running on oeis4.)