A076990 a(1) = 1, a(2) = 2; thereafter a(n) = smallest number not occurring earlier such that the sum of three successive terms is prime.

1, 2, 4, 5, 8, 6, 3, 10, 16, 11, 14, 12, 15, 20, 18, 9, 26, 24, 17, 30, 32, 21, 36, 22, 13, 38, 28, 7, 44, 46, 19, 42, 40, 25, 48, 34, 27, 52, 58, 29, 50, 60, 39, 64, 54, 31, 66, 70, 37, 56, 74, 33, 72, 62, 23, 78, 80, 35, 76, 68, 47, 82, 94, 51, 84, 88, 55, 86, 92, 45, 90, 98

Offset: 1

Author

Amarnath Murthy, Oct 25 2002

Keywords

• nonn

Comments

a(n) = n only for n: 1, 2, 6, 12 for all n < 10000. - Robert G. Wilson v, Nov 21 2012

a(n) = ~(1 +- 2/5)*n. - Robert G. Wilson v, Nov 21 2012

a(n) is odd if and only if n == 1 (mod 3). - Robert Israel, Dec 09 2015

The odd terms grow according to a(3k+1) ~ 2k and the even terms according to a(n) ~ 4n/3. - M. F. Hasler, Dec 11 2015

Examples

			After 8 and 6 the next term is 3 as 8+6+3 = 17 is a prime.
		

Links

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

Crossrefs

Cf. A076045, A073653, A219533.

See also A055265.

Programs

Maple

N:= 200: # to get all terms before the first > N
V:= Vector(N):
V[1]:= 1: V[2]:= 1:
A[1]:= 1: A[2]:= 2:
m0:= 3: m:= 0:
for n from 3 while m <= N do
   t:= A[n-1]+A[n-2];
   m1:= m0 + (m0+t+1 mod 2);
   for m from m1 to N by 2 do if isprime(m+t) and V[m] = 0 then
       A[n]:= m;
       V[m]:= 1;
       break;
   fi od:
   if m = m0 then
       while m0 < N and V[m0] = 1  do m0:= m0+1 od:
   fi;
od:
seq(A[j],j=1..n-2); # Robert Israel, Dec 09 2015

Mathematica

f[s_List] := Block[{p = s[[-2]] + s[[-1]], q = 1}, While[ !PrimeQ[p + q] || MemberQ[s, q], q++]; Append[s, q]]; Nest[f, {1, 2}, 70] (* Robert G. Wilson v, Nov 21 2012 *)

PARI

A076990(n,verbose=0/*=1 to print all terms*/,a=1,u=0,m=1,L=0)={for(i=2,n,verbose&&print1(a",");u+=1<M. F. Hasler, Dec 11 2015

Extensions

More terms from David Garber, Oct 30 2002