A355009 -id:A355009 - cp's OEIS frontend

A354972 Numbers k such that A354975(k) is prime.

2, 9, 15, 19, 21, 32, 63, 75, 77, 108, 115, 120, 147, 151, 229, 235, 243, 248, 252, 258, 279, 283, 285, 288, 290, 299, 303, 309, 314, 352, 360, 361, 362, 377, 382, 387, 393, 398, 413, 418, 430, 447, 457, 462, 465, 467, 468, 470, 475, 488, 510, 518, 551, 560, 569, 604, 625, 643, 679, 732, 735, 740

Offset: 1

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

nonn

Numbers k such that Sum_{i=1..k} (prime(i+k) mod prime(i)) is prime.

			a(1) = 2 is a term because A354975(2) = (5 mod 2) + (7 mod 3) = 2 is prime.

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

Cf. A354975, A355009.

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

isok(k) = isprime(sum(i=1, k, prime(i+k) % prime(i))); \\ Michel Marcus, Jun 19 2022

from itertools import count, islice
from sympy import prime, isprime
def A354972_gen(): # generator of terms
    for n in count(1):
        if isprime(sum(prime(i+n) % prime(i) for i in range(1,n+1))):
            yield n
A354972_list = list(islice(A354972_gen(),10)) # Chai Wah Wu, Jun 20 2022

A354975 a(n) = Sum_{i=1..n} (prime(i+n) mod prime(i)).

Original entry on oeis.org

1, 2, 6, 9, 16, 26, 25, 46, 47, 54, 81, 112, 140, 116, 173, 215, 254, 234, 317, 329, 409, 440, 511, 584, 581, 582, 666, 649, 776, 866, 875, 967, 1057, 1152, 1310, 1419, 1246, 1294, 1296, 1551, 1599, 1722, 1970, 2152, 2166, 2154, 2338, 2396, 2523, 2831, 3120, 2867, 3220, 3332, 3274, 3266, 3462

Offset: 1

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

nonn

			For n = 3, a(n) = (7 mod 2) + (11 mod 3) + (13 mod 5) = 1+2+3 = 6.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000040, A207409, A354972, A355009.

f:= proc(n) local k;
   add(ithprime(n+k) mod ithprime(k),k=1..n)
end proc:
map(f, [$1..100]);

a[n_]:=Sum[Mod[Prime[i+n],Prime[i]],{i,n}]; Array[a,57] (* Stefano Spezia, Jun 15 2022 *)

a(n) = sum(i=1, n, prime(i+n) % prime(i)); \\ Michel Marcus, Jun 15 2022

from sympy import prime
def A354975(n): return sum(prime(i+n) % prime(i) for i in range(1,n+1)) # Chai Wah Wu, Jun 19 2022

cp's OEIS Frontend

A354972 Numbers k such that A354975(k) is prime.

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