A351693 a(n) is the least prime prime(k) for which A351692(k) = n, or 0 if there is no such prime.

2, 3, 29, 13, 47, 19, 31, 647, 101, 107, 181, 569, 109, 839, 199, 811, 283, 373, 97, 73, 151, 79, 229, 149, 103, 443, 401, 701, 167, 751, 1901, 347, 379, 197, 157, 227, 673, 193, 383, 277, 353, 991, 313, 359, 419, 337, 911, 461, 1319, 1279, 349, 757, 2957, 1747, 827, 631, 457, 1511, 1249, 1559, 1091

Offset

0,1

Comments

a(n) = prime(k) for the least k such that prime(k)+2*prime(k+j) and prime(k)+2*prime(k-j) are both prime for j = n but not both prime for j = 1 ... n-1.

Links

Robert Israel, Table of n, a(n) for n = 0..1000

Example

a(3) = 13 = prime(6) because A351692(6) = 3 and A351692(k) <> 3 for 1 <= k < 6.

Maple

nP:= 10000: Primes:= [seq(ithprime(i), i=1..nP)]: R:= 2: found:= true:
for n from 1 to 300 while found do
found:= false;
  for k from n+1 to nP-n do
    if isprime(Primes[k]+2*Primes[k-n]) and isprime(Primes[k]+2*Primes[k+n]) and
      andmap(t -> not isprime(Primes[k]+2*Primes[k-t]) or not
        isprime(Primes[k]+2*Primes[k+t]), [$1..n-1]) then
        R:= R, Primes[k]; found:= true; break
    fi
od od:
R;

Prog

(PARI) f(n) = for (k=1, n-1, my(p=prime(n)); if (isprime(p + 2*prime(n-k)) && isprime(p + 2*prime(n+k)), return(k))); return(0); \\ A351692
a(n) = my(k=1); while (f(k) != n, k++); prime(k); \\ Michel Marcus, May 11 2022

Crossrefs

Cf. A000040, A351692.

Sequence in context: A003017 A096580 A371024 * A324941 A028868 A081332

Adjacent sequences: A351690 A351691 A351692 * A351694 A351695 A351696

Keyword

nonn

Author

J. M. Bergot and Robert Israel, May 05 2022

Status

approved