A339238 a(1)=a(2)=1 and, for n >= 3, a(n) = a(n-1) + a(n-2) - Sum_{i=3..k} primepi(a(n-i)), where k is the largest integer such that a(n) >=2 and not already in the sequence.

1, 1, 2, 3, 5, 7, 9, 10, 12, 11, 15, 13, 14, 16, 18, 22, 28, 19, 20, 30, 25, 39, 21, 33, 42, 36, 38, 50, 45, 40, 23, 34, 57, 29, 54, 35, 17, 52, 58, 66, 49, 77, 92, 61, 68, 51, 101, 37, 8, 45, 41, 44, 55, 72, 70, 43, 93, 67, 91, 120, 85, 105, 117, 69, 63, 75

Offset

1,3

Links

Table of n, a(n) for n=1..66.

Formula

a(n) = a(n-1) + a(n-2) - Sum_{i=3..k} primepi(a(n-i)), where a(1)=a(2)=1 and k<=n-3 such that a(n) >= 2 and not in {a(i), i=1..n-1}.

Prog

(Python)
from sympy import primepi
a_1 = a_2 = 1
print(a_2, "\n", a_1)
list1 = [a_1, a_2]
for n in range(3, 1001):
    a = a_1 + a_2
    i = 2
    while i < len(list1):
        d = a - primepi(list1[i])
        if d >= 2 and d not in list1: a = d
        else: break
        i += 1
    list1.insert(0, a)
    a_2 = a_1
    a_1 = a
    print(a)

Crossrefs

Cf. A000045, A000720, A005132.

Sequence in context: A117284 A137377 A274793 * A168543 A026277 A201804

Adjacent sequences: A339235 A339236 A339237 * A339239 A339240 A339241

Keyword

nonn

Author

Ya-Ping Lu, Nov 28 2020

Status

approved