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

1,2

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

Links

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

Example

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

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 *)

Prog

(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<<a; while(bittest(u, m), m++); my(s=L+a); L=a; forprime(p=s+m, , bittest(u, p-s)&&next; a=p-s; break)); a}\\ could be made more efficient using Israel's comment and a second "m" for the (smallest possible) even terms. - M. F. Hasler, Dec 11 2015

Crossrefs

Cf. A076045, A073653, A219533.

See also A055265.

Sequence in context: A110991 A262942 A352808 * A330434 A330424 A057168

Adjacent sequences: A076987 A076988 A076989 * A076991 A076992 A076993

Keyword

nonn

Author

Amarnath Murthy, Oct 25 2002

Extensions

More terms from David Garber, Oct 30 2002

Status

approved