

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.


4



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
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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[n1]+A[n2];
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..n2); # 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, ps)&&next; a=ps; 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: A101410 A110991 A262942 * A057168 A087711 A123128
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



