A355009 Primes in A354975.

2, 47, 173, 317, 409, 967, 3877, 6173, 6449, 14401, 16477, 18257, 28183, 30119, 73561, 76607, 86579, 90227, 92867, 97987, 110777, 112663, 114749, 117671, 121553, 130069, 136033, 141403, 144671, 190891, 205129, 207301, 208283, 216481, 221677, 229199, 235337, 231223, 261347, 265123, 281191, 311473

Offset: 1

Author

J. M. Bergot and Robert Israel, Jun 15 2022

Keywords

• nonn

Comments

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).

Examples

			a(3) = A354975(15) = 173 is the third member of A354975 that is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A354972, A354975.

Programs

Maple

f:= proc(n) local k;
   add(ithprime(n+k) mod ithprime(k), k=1..n)
end proc:
select(isprime, map(f, [$1..1000]);

Mathematica

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 *)

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

Python

from itertools import count, islice
from sympy import prime, isprime
def A355009_gen(): # generator of terms
    return filter(isprime,(sum(prime(i+n) % prime(i) for i in range(1,n+1)) for n in count(1)))
A355009_list = list(islice(A355009_gen(),5)) # Chai Wah Wu, Jun 20 2022

Formula

a(n) = A354975(A354972(n)).