A395307 Let p1 and p2 be two consecutive primes. Take the sums p1*10^j+p2, with 0<=j<=(number of digits of p2), and p2*10^j+p1, with 1<=j<=(number of digits of p1). Sequence lists the least prime p1 that together with its successor p2 generates exactly n distinct primes through the described process.

3, 2, 31, 233, 211, 2861, 10711, 99611, 513053, 5486807, 184700947, 1002002467, 1232268241, 143042268079, 844598501179, 9899150975347, 18197101446031

Offset

1,1

Links

Table of n, a(n) for n=1..17.

Paolo P. Lava, Terms and generated primes

Carlos Rivera, Puzzle 1265 A sort of "convolution" between a prime P1 and its successor P2, The Prime Puzzles and Problems Connection.

Example

a(1) = 3 -> p1 = 3, p2 = 5; 3 + 5 = 8 (not prime), 30 + 5 = 35 (not prime), 50 + 3 = 53 (prime).
a(2) = 2 -> p1 = 2, p2 = 3; 2 + 3 = 5 (prime), 20 + 3 = 23 (prime), 30 + 2 = 32 (not prime).
a(3) = 31 -> p1 = 31, p2= 37; 31 + 37 = 68 (not prime), 310 + 37 = 347 (prime), 3100 + 37 = 3137 (not prime), 370 + 31 = 401 (prime), 3700 + 31 = 3731 (prime).

Prog

(PARI) isok(p, q, n) = my(vnp = vector(#digits(q)+1, j, p*10^(j-1)+q), vnq = vector(#digits(p), j, q*10^j+p)); #setunion(Set(select(isprime, vnp)), Set(select(isprime, vnq))) == n;
a(n) = my(p=2, q=nextprime(p+1)); while (!isok(p, q, n), p=q; q=nextprime(p+1)); p; \\ Michel Marcus, Apr 25 2026

Crossrefs

Cf. A000040, A394773.

Sequence in context: A054676 A181994 A350023 * A353123 A154332 A375409

Adjacent sequences: A395304 A395305 A395306 * A395308 A395309 A395310

Keyword

nonn,hard,more

Author

Paolo P. Lava, Apr 19 2026

Status

approved