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A355009 Primes in A354975.

%I A355009 #16 Jun 20 2022 15:39:54
%S A355009 2,47,173,317,409,967,3877,6173,6449,14401,16477,18257,28183,30119,
%T A355009 73561,76607,86579,90227,92867,97987,110777,112663,114749,117671,
%U A355009 121553,130069,136033,141403,144671,190891,205129,207301,208283,216481,221677,229199,235337,231223,261347,265123,281191,311473
%N A355009 Primes in A354975.
%C A355009 Primes are in the order in which they appear in A354975, so the sequence is not increasing: for example, a(37) = 235337 > 231223 = a(38).
%H A355009 Robert Israel, <a href="/A355009/b355009.txt">Table of n, a(n) for n = 1..1000</a>
%F A355009 a(n) = A354975(A354972(n)).
%e A355009 a(3) = A354975(15) = 173 is the third member of A354975 that is prime.
%p A355009 f:= proc(n) local k;
%p A355009    add(ithprime(n+k) mod ithprime(k), k=1..n)
%p A355009 end proc:
%p A355009 select(isprime, map(f, [$1..1000]);
%t A355009 Block[{nn = 450, a, p}, Do[Set[p[i], Prime[i]], {i, 2 nn}]; Reap[Do[If[PrimeQ[#], Sow[#]] &@ Sum[Mod[p[i + j], p[j]], {j, i}], {i, nn}]][[-1, -1]]] (* _Michael De Vlieger_, Jun 19 2022 *)
%o A355009 (PARI) lista(nn) = my(list=List()); for (n=1, nn, if (isprime(p=sum(i=1, n, prime(i+n) % prime(i))), listput(list, p));); Vec(list); \\ _Michel Marcus_, Jun 19 2022
%o A355009 (Python)
%o A355009 from itertools import count, islice
%o A355009 from sympy import prime, isprime
%o A355009 def A355009_gen(): # generator of terms
%o A355009     return filter(isprime,(sum(prime(i+n) % prime(i) for i in range(1,n+1)) for n in count(1)))
%o A355009 A355009_list = list(islice(A355009_gen(),5)) # _Chai Wah Wu_, Jun 20 2022
%Y A355009 Cf. A354972, A354975.
%K A355009 nonn
%O A355009 1,1
%A A355009 _J. M. Bergot_ and _Robert Israel_, Jun 15 2022