A082433 a(n) = A072181(n) - p, where p is the largest prime < A072181(n) - 1.

3, 5, 7, 7, 11, 11, 11, 11, 13, 23, 17, 17, 17, 41, 191, 47, 31, 53, 53, 53, 31, 179, 61, 61, 337, 131, 523, 523, 419, 223, 223, 223, 223, 79, 3821, 3821, 3821, 23399, 21269, 21269, 3607

Offset: 3

Author

Naohiro Nomoto, Apr 25 2003

Keywords

• nonn
• more

Comments

Are all terms prime?

All terms are odd. - Michael S. Branicky, Sep 05 2021

Examples

			a(4) = A072181(4)-7 = 12-7 = 5.
		

Crossrefs

Cf. A005235, A037153, A037155, A072181, A082432.

Programs

Python

from sympy import factorint, isprime
def afindn(terms):
    prev_factors, prevan, prevk, n = dict(), 1, None, 2
    for n in range(2, terms+1):
        n_factors, an = factorint(n), 1
        for pi in set(prev_factors.keys()) | set(n_factors.keys()):
            ei = prev_factors[pi] if pi in prev_factors else 1
            fi = n_factors[pi] if pi in n_factors else 1
            an *= pi**(ei*fi)
        if n >= 3:
            if an != prevan:
                k = 3
                while not isprime(an - k): k += 2
            else:
                k = prevk
            print(k, end=", ")
            prevk = k
        prev_factors, prevan = factorint(an), an
afindn(36) # Michael S. Branicky, Sep 05 2021

Extensions

a(36)-a(40) from Jinyuan Wang, Sep 05 2020

a(41)-a(43) from Michael S. Branicky, Sep 05 2021