A213981 a(n) = the least prime p > prime(n+1) such that (p mod prime(n)) + (p mod prime(n+1)) is prime.

5, 7, 11, 19, 23, 31, 53, 61, 47, 59, 71, 79, 83, 223, 97, 109, 179, 131, 139, 359, 149, 241, 167, 179, 199, 509, 211, 431, 331, 227, 643, 263, 827, 283, 449, 311, 317, 823, 337, 349, 359, 367, 383, 787, 593, 401, 439, 673, 683, 691, 467, 479, 487, 769, 523, 1061, 809, 1093, 1117, 563, 571, 587, 619, 1559, 2203, 641, 673, 1021

Offset

1,1

Comments

Corresponding primes are 3,3,5,13,11,19,17,19,19,29,43,43,41,43,47,53,59 (s1).

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Example

5 mod 2 + 5 mod 3 = 1 + 2 = 3 (prime)
7 mod 3 + 7 mod 5 = 1 + 2 = 3 (prime)
19 mod 7 + 19 mod 11 = 5 + 8 = 13 (prime)

Mathematica

s=Reap[Do[Sow[Select[Prime[Range[n+2, 1000]], PrimeQ[Mod[#, Prime[n]]+ Mod[#, Prime[n+1]]]&][[1]]], {n, 70}]][[2, 1]]
s1=Table[Mod[s[[n]], Prime[n]]+ Mod[s[[n]], Prime[n+1]], {n, 70}]

Prog

(PARI)
a(n)={my(pn=prime(n)); my(pnp1=nextprime(pn+1)); my(p=nextprime(pnp1+1));
while(!isprime(p%pn + p%pnp1), p=nextprime(p+1)); p} \\ Andrew Howroyd, Feb 25 2018

Crossrefs

Sequence in context: A240849 A116641 A288446 * A273048 A240621 A040127

Adjacent sequences: A213978 A213979 A213980 * A213982 A213983 A213984

Keyword

nonn

Author

Zak Seidov, Feb 16 2013

Status

approved