A352952 - OEIS

A352952

a(1) = 3; a(2) = 5; a(n+1) = a(n) + b(n), where b(n) = max {a(n-1)+-1, a(n-2)+-1, a(n-3)+-1, ..., a(1)+-1} such that a(n) + b(n) is a prime.

3, 5, 7, 13, 19, 31, 43, 73, 103, 109, 211, 313, 523, 733, 751, 1483, 1693, 1801, 2551, 4243, 6793, 9343, 10093, 10303, 12853, 14653, 17203, 19753, 22303, 24103, 25903, 26113, 28663, 28771, 54673, 83443, 112213, 140983, 169753, 171553, 200323, 229093, 257863

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OFFSET

1,1

COMMENTS

This sequence is finite and has 111 terms, which are given in the b-file.

a(n) == 1 (mod 6) if n > 2. For n = 3 or > 4, b(n) = a(n-i) - 1, where 1 < b < n.

LINKS

Ya-Ping Lu, Table of n, a(n) for n = 1..111

EXAMPLE

For n = 6, the first 6 terms are [3, 5, 7, 13, 19, 31] and, in the list [19+-1, 13+-1, 7+-1, 5+-1, 3+-1], 13-1 is the largest number that gives a prime when added to a(6). Thus, b(6) = 13 - 1 = 12 and b(7) = a(6) + b(6) = 43.

PROG

(Python)

from sympy import isprime; L = [3, 5]

while 1:

for j in range(2, len(L)+1):

s = L[-1] + L[-j]

if isprime(s+1): L.append(s+1); break

elif isprime(s-1): L.append(s-1); break

else: break

print(*L, sep = ', ')

CROSSREFS

Cf. A337347.