A276141 a(1)=2; thereafter a(n) is the least prime > a(n-1) such that 2*a(n-1)+a(n) is a prime.

2, 3, 5, 7, 17, 19, 23, 37, 53, 61, 71, 97, 113, 127, 167, 223, 227, 229, 233, 277, 353, 397, 419, 421, 449, 463, 503, 547, 563, 571, 599, 613, 641, 691, 701, 709, 719, 769, 773, 787, 797, 823, 827, 877, 929, 1021, 1187, 1249, 1409, 1423, 1427, 1429

Offset

1,1

Comments

Corresponding values of 2*a(n-1)+a(n): 7, 11, 17, 31, 53, 61, 83, 127, 167, 193, 239, 307, 353, 421, 557, 673, 683, 691, 743, 907, 1103, ...

a(n) == (-1)^n (mod 3) for n <> 2. - Robert Israel, Sep 02 2016

Conjecture: starting with any other prime, the sequence will eventually merge with this one. - Zak Seidov, Aug 06 2023.

Links

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

Maple

A[1]:= 2:
for n from 2 to 100 do
  p:= nextprime(A[n-1]);
  while not isprime(2*A[n-1]+p) do p:= nextprime(p) od:
  A[n]:= p
od:
seq(A[i], i=1..100); # Robert Israel, Sep 02 2016

Mathematica

s={2, 3}; a=3; Do[k=2; While[!PrimeQ[2a+a+k]||!PrimeQ[a+k], k=2+k]; a=a+k; AppendTo[s, a], {50}]; s

Prog

(PARI) terms(n) = my(x=2, i=0); while(1, if(n==0, break({2}), print1(x, ", "); if(n==1, break({2}), forprime(p=x+1, , if(i==n-1, break({2})); if(ispseudoprime(2*x+p), print1(p, ", "); x=p; i++)))))
/* The following function call prints the initial 50 terms */
terms(50) \\ Felix Fröhlich, Aug 22 2016

Crossrefs

Sequence in context: A042995 A108222 A090725 * A214588 A089968 A164060

Adjacent sequences: A276138 A276139 A276140 * A276142 A276143 A276144

Keyword

nonn

Author

Zak Seidov, Aug 22 2016

Status

approved