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fini,nonn,full,changed

This sequence is finite and the rest of the terms, a(44) through a(111) are: 286633, 288433, 290233, 290443, 292993, 294793, 294799, 589591, 878023, 906793, 909343, 1204141, 2082163, 2376961, 2667193, 2961991, 5338951, 5631943, 8593933, 13932883, 16894873, 22233823, 25195813, 26399953, 26400163, 29362153, 32324143, 32324251, 61686403, 67025353, 67320151, 134345503, 136722463, 204042613, 236366863, 238743823, 271068073, 276407023, 343727173, 346689163, 352028113, 384352363, 451672513, 451672621, 798361783, 1250034403, 1701707023, 2153379643, 2156341633, 2188665883, 2188694653, 2221018903, 2226357853, 2229319843, 2230523983, 2230524193, 2262848443, 2268187393, 2271149383, 2271444181, 4497802033, 4949474653, 7220918833, 7288238983, 7320563233, 9592007413, 9592009963, 9592599553.

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

Ya-Ping Lu, <a href="/A352952/b352952.txt">Table of n, a(n) for n = 1..111</a>

fini,nonn,changed

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For n = 6, a(1) through a(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 first element largest number that gives a prime number when added to a(6), and thus . Thus, b(6) = 13 - 1 = 12 and b(7) = a(6) + b(6) = 43.

allocated for Ya-Ping Lu

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

1,1

This sequence is finite and the rest of the terms, a(44) through a(111) are: 286633, 288433, 290233, 290443, 292993, 294793, 294799, 589591, 878023, 906793, 909343, 1204141, 2082163, 2376961, 2667193, 2961991, 5338951, 5631943, 8593933, 13932883, 16894873, 22233823, 25195813, 26399953, 26400163, 29362153, 32324143, 32324251, 61686403, 67025353, 67320151, 134345503, 136722463, 204042613, 236366863, 238743823, 271068073, 276407023, 343727173, 346689163, 352028113, 384352363, 451672513, 451672621, 798361783, 1250034403, 1701707023, 2153379643, 2156341633, 2188665883, 2188694653, 2221018903, 2226357853, 2229319843, 2230523983, 2230524193, 2262848443, 2268187393, 2271149383, 2271444181, 4497802033, 4949474653, 7220918833, 7288238983, 7320563233, 9592007413, 9592009963, 9592599553.

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

For n = 6, a(1) through a(6) 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 first element that gives a prime number when added to a(6), and thus b(6) = 13 - 1 = 12 and b(7) = a(6) + b(6) = 43.

(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 = ', ')

Cf. A337347.

allocated

nonn

Ya-Ping Lu, Apr 10 2022

approved

editing