A062044 -id:A062044 - cp's OEIS frontend

A062042 a(1) = 2, a(n) = least number greater than a(n-1) such that a(n-1) + a(n) is a prime.

2, 3, 4, 7, 10, 13, 16, 21, 22, 25, 28, 31, 36, 37, 42, 47, 50, 51, 52, 55, 58, 69, 70, 79, 84, 89, 90, 91, 100, 111, 112, 115, 118, 121, 130, 133, 136, 141, 142, 151, 156, 157, 160, 171, 176, 177, 182, 185, 188, 191, 192, 197, 200, 201, 208, 211, 220, 223, 226

Offset: 1

Amarnath Murthy, Jun 05 2001

			a(5) = 10 and the least number more than 10 that gives a prime when increased by 10 is 13, 13 + 10 = 23.

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

Cf. A062044.

A[1]:= 2;
for n from 2 to 100 do
  A[n]:= nextprime(2*A[n-1])-A[n-1]
od:
seq(A[n],n=1..100); # Robert Israel, Aug 28 2018

a=2;lst={a};Do[b=a+1;While[ !PrimeQ[a+b],b++ ];AppendTo[lst,b];a=b,{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)
NestList[NextPrime[2#]-#&,2,60] (* Harvey P. Dale, Jul 20 2011 *)

FirstTerms(n)={my(x=2,y,a=vector(n),j=1);a[1]=2;while(j++<=n,y=x+1;while(!isprime(x+y),y++);x=y;a[j]=y);return(a)} \\ R. J. Cano, Jan 18 2017

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

A213815 Arithmetic mean of next a(n) successive nonnegative integers is prime.

Original entry on oeis.org

5, 1, 3, 5, 7, 5, 7, 9, 3, 5, 7, 5, 11, 1, 11, 9, 7, 1, 3, 5, 7, 21, 3, 17, 11, 9, 3, 1, 19, 21, 3, 5, 7, 5, 19, 5, 7, 9, 3, 17, 11, 1, 7, 21, 11, 1, 11, 5, 7, 5, 3, 9, 7, 1, 15, 5, 19, 5, 7, 9, 3, 5, 19, 5, 11, 9, 15, 25, 7, 5, 7, 9, 11, 1, 11, 5, 7, 1, 3

Offset: 1

Alex Ratushnyak, Jul 18 2012

Corresponding primes: A062044(n).

			(0+1+2+3+4)/5 = 2 is prime, so a(1)=5,
then 5/1 = 5 is prime, so a(2)=1,
then (6+7+8)/3 = 7 is prime, so a(3)=3.

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

Cf. A000040, A062044, A214362.

R:= 5: count:= 1: r:= 4:
for count from 2 to 100 do
    s:= nextprime(r);
    R:= R,2*(s-r)-1;
    r:= 2*s - r - 1;
od:
R; # Robert Israel, Feb 28 2025

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

Original entry on oeis.org

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

Alex Ratushnyak, Jul 18 2012

Corresponding primes: A062044(n).

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

			(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.

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

Cf. A000040, A062042, A062044, A213815.

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

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

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

cp's OEIS Frontend

A062042 a(1) = 2, a(n) = least number greater than a(n-1) such that a(n-1) + a(n) is a prime.

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A213815 Arithmetic mean of next a(n) successive nonnegative integers is prime.

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

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