A340564 - OEIS

%I #9 Jan 11 2021 23:08:03

%S 5,13,23,113,137,151,163,251,317,461,479,487,521,661,691,719,887,907,

%T 991,1129,1213,1453,1901,1949,1987,2053,2141,2243,2333,2399,2549,2797,

%U 3041,3049,3119,3221,3433,3457,3527,3529,3691,3697,3911,4013,4241,4649,4817,5099,5407,5413,5689,5693,6217

%N Primes p such that the sum of (p mod q) for primes q < p is prime.

%C a(n) = prime(m) if A033955(m) is prime.

%H Robert Israel, <a href="/A340564/b340564.txt">Table of n, a(n) for n = 1..4000</a>

%e a(3) = 23 is a term because (23 mod 2) + ... + (23 mod 19) = 1+2+3+2+1+10+6+4 = 29 is prime.

%p f:= proc(n) local i,p;

%p   p:= ithprime(n);

%p   add(p mod ithprime(i),i=1..n-1)

%p end proc:

%p map(ithprime, select(t -> isprime(f(t)), [$1..2000]));

%o (PARI) isok(p) = if (isprime(p), my(s=0); forprime(q=2, precprime(p-1), s += p % q); isprime(s);); \\ _Michel Marcus_, Jan 11 2021

%Y Cf. A033955.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 11 2021