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A354154
a(1) = 0; for n>1, a(n) = prime(n-1) - A090252(n).
2
0, 0, 0, 0, 3, 4, 4, 6, 6, 6, 21, 12, 14, 16, 22, 18, 22, 22, 20, 24, 24, 20, 63, 24, 28, 30, 30, 30, 52, 30, 86, 78, 48, 48, 42, 48, 48, 50, 54, 54, 46, 48, 44, 52, 44, 46, 173, 54, 60, 60, 56, 54, 58, 50, 58, 60, 64, 58, 186, 156, 58, 56, 236, 78, 150, 80, 78, 90, 86, 90, 86, 84, 88, 90, 92, 96, 90, 82, 86, 88, 92, 88, 84, 84, 84, 86, 84, 82, 84
OFFSET
1,5
COMMENTS
Theorem: a(n) >= 0 for all n.
LINKS
EXAMPLE
A090252 begins
1, 2, 3, 5, 4, 7, 9, 11, 13, ...
and we subtract these numbers from
1, 2, 3, 5, 7, 11, 13, 17, 19, ...
to get
0, 0, 0, 0, 3, 4, 4, 6, 6, ...
PROG
(Python)
from math import gcd, prod
from sympy import isprime, nextprime
from itertools import count, islice
def agen(): # generator of terms
alst, aset, mink, p = [1], {1}, 2, 1
yield 0
for n in count(2):
k, s, p = mink, n - n//2, nextprime(p)
prodall = prod(alst[n-n//2-1:n-1])
while k in aset or gcd(prodall, k) != 1: k += 1
alst.append(k); aset.add(k); yield p - k
while mink in aset: mink += 1
print(list(islice(agen(), 89))) # Michael S. Branicky, May 28 2022
CROSSREFS
Cf. A090252.
Sequence in context: A255171 A323712 A215250 * A229022 A014683 A213222
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 28 2022
STATUS
approved