A076697 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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

Table of n, a(n) for n=0..53.

Ron Knott, Lucas numbers.

Douglas S. McNeil, in reply to Robert Israel, A076697, SeqFan google group, April 9, 2025.

PROG

(PARI) A076697_first(n, m=0)=vector(n, i, i>1 || n=-1; until(m<m=max(A079451(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