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A338134
Initial terms are the first 11 odd prime numbers. After that each new term in the sequence is the sum of whichever subset of the previous 11 terms gives the smallest prime number that is larger than the largest term so far.
2
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 67, 71, 83, 97, 109, 127, 131, 149, 167, 179, 197, 251, 263, 307, 337, 367, 443, 587, 653, 683, 743, 797, 821, 907, 1087, 1291, 1493, 2003, 2237, 2243, 2333, 2447, 2791, 3019, 3691, 4583, 4787, 6287
OFFSET
1,1
COMMENTS
The sequence is finite with the final term a(1022) having 94 decimal digits.
Instead of 11, other choices k of the number of initial odd primes and number of previous terms to consider when picking the next prime give different sequence lengths L and final terms m. Values are shown in the following table.
=======================================================
k L log(m) m
-----+-------------------------------------------------
4 | 13 6.42 53
5 | 18 7.77 2377
6 | 26 8.42 4547
7 | 66 19.32 246069541
8 | 176 46.61 174401554254658978301
9 | 313 74.93 348416283338512248746770398000349
10 | 657 155.19 25092330625366012736545948...
11 | 1022 214.78 18914773701982111040121422...
12 | 2575 596.03 71213007235221948920803479...
13 | 5142 1172.46 15648776898352974934674946...
LINKS
PROG
(PARI)
F(u, m, test)={my(recurse(k, s, b)=if(s<b, if(s>m&&test(s), b=s); while(k<#u, k++; b=self()(k, s+u[k], b))); b); recurse(0, 0, oo)}
lista(n, k=11)={my(v=vector(k)); for(r=1, n, my(t=if(r<=k, prime(r+1), F(v, v[#v], ispseudoprime))); print1(t, ", "); if(t==oo, break); v=concat(v[2..k], t))}
{ lista(60) } \\ Andrew Howroyd, Oct 13 2020
CROSSREFS
Cf. A065091.
Sequence in context: A215697 A322184 A245072 * A138980 A191378 A191376
KEYWORD
nonn,fini,full
AUTHOR
STATUS
approved