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A226027 a(n) is the largest prime that is a sum of some 3 distinct previous terms. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)