A354154 a(1) = 0; for n>1, a(n) = prime(n-1) - A090252(n).

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

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A354151 A354152 A354153 * A354155 A354156 A354157

Keyword

nonn

Author

N. J. A. Sloane, May 28 2022

Status

approved