A076697 Indices of record values in A079451, largest prime factor of Lucas numbers A000032.

0, 2, 4, 5, 7, 8, 11, 13, 16, 17, 19, 26, 31, 37, 41, 47, 53, 61, 68, 71, 76, 79, 86, 113, 136, 164, 172, 178, 202, 218, 229, 262, 278, 284, 307, 313, 328, 353, 373, 436, 443, 458, 487, 503, 557, 577, 586, 613, 617, 746, 751, 758, 863, 914

Offset: 0

Author

Shane Findley, Oct 25 2002

Keywords

• nonn

Comments

From M. F. Hasler, Apr 09 2025: (Start)

Original name: Next-to-largest factor of Lucas(n).

The offset 0 is coherent with the fact that the initial term is a starting value rather than a record value.

When A000032(n) is prime (<=> n is in A001606), it necessarily sets a new record for the largest prime factor, since A000032 is increasing from the second term on. Therefore, A001606 is a subsequence. (End)

Links

• Ron Knott, Lucas numbers.
• Douglas S. McNeil, in reply to Robert Israel, A076697, SeqFan google group, April 9, 2025.

Crossrefs

Cf. A000042 (Lucas numbers, starting with 2), A079451 (largest prime factor of these).

Cf. A001606 (Indices of prime Lucas numbers: a subsequence).

Programs

PARI

A076697_first(n, m=0)=vector(n,i, i>1 || n=-1; until(mA079451(n++), m), );n) \\ M. F. Hasler, Apr 09 2025

Python

def A076697(n):
    try: terms, M = A076697.terms, A076697.M
    except AttributeError: A076697.terms = terms = [0]; A076697.M = M = 2
    while len(terms) <= n: terms.append(next(i for i in range(terms[-1]+1, 1<<59)
        if M < (M:=max(A079451(i),M)))); A076697.M = M
    return terms[n] # M. F. Hasler, Apr 10 2025

Extensions

New definition and data corrected and extended by M. F. Hasler, Apr 09 2025