A226027 a(n) is the largest prime that is a sum of some 3 distinct previous terms.

5, 7, 11, 23, 41, 71, 101, 179, 257, 443, 521, 971, 1499, 2477, 2927, 3191, 3719, 6917, 9851, 13577, 16061, 25919, 39503, 53087, 56813, 96323, 149417, 245747, 342077, 491501, 494699, 986207, 1231961, 1726667, 2068751, 2165081, 4233839, 5220053, 5714759, 7879847

Offset

1,1

Comments

Initial terms {2,3,5} and {3,5,7} give no prime, hence we start with a(1..3) = {5, 7, 11}.

Is the sequence infinite?

The Mathematica program is fast because it uses that fact that 7 must be one of the three numbers in the sum. Note that p = 5 (mod 6) for all terms but 7. - T. D. Noe, May 24 2013

Links

Zak Seidov and T. D. Noe, Table of n, a(n) for n = 1..500 (first 123 from Zak Seidov)

Mathematica

t = {5, 11}; Do[u = Subsets[t, {2}]; w = Reverse[Sort[7 + Total /@ u]]; s = Select[w, PrimeQ, 1]; mx = s[[1]]; AppendTo[t, mx], {97}]; t = Insert[t, 7, 2] (* T. D. Noe, May 24 2013 *)

Prog

(PARI) N=50; v=vector(N); v[1]=5; v[2]=7; v[3]=11; n=3; while(n<N, m=0; for(i=1, n, for(j=i+1, n, for(k=j+1, n, t=v[i]+v[j]+v[k]; if(t>m && isprime(t), m=t)))); if(m>0, n++; v[n]=m)); v /* from Ralf Stephan */

Crossrefs

Sequence in context: A266233 A124111 A151715 * A090810 A092307 A005385

Adjacent sequences: A226024 A226025 A226026 * A226028 A226029 A226030

Keyword

nonn

Author

Zak Seidov, May 23 2013

Status

approved