A199407 -id:A199407 - cp's OEIS frontend

A193948 Integers k such that for all i > k the largest prime factor of i(i+1)(i+2)(i+3)(i+4)(i+5)(i+6) exceeds the largest prime factor of k(k+1)(k+2)(k+3)(k+4)(k+5)(k+6).

4, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 184, 527, 4896, 11658, 12874, 18904, 41919, 45998, 48504, 50688, 51982, 356207, 426851, 960750, 1961725, 4604094, 8418495, 10811745, 32963628, 45249999, 569800611, 7374557947, 121153257533

Offset: 1

Andrey V. Kulsha, Aug 10 2011

nonn

Currently terms through a(16) = 12874 have been proved to be correct, while remaining terms are conjectural. Stormer's theorem (see link) provides an approach to proving their correctness. Such an approach should be easy for the first few terms. - Franklin T. Adams-Watters, Nov 07 2011

Andrey V. Kulsha, Table of n, a(n) for n = 1..39
Wikipedia, Stormer's theorem

Cf. A145606, A193947, A199407.

A200566 Integers n such that for all i > n the largest prime factor of product(i+k, {k,0,8}) exceeds the largest prime factor of product(n+k, {k,0,8}).

Original entry on oeis.org

2, 4, 8, 10, 14, 20, 22, 28, 32, 34, 38, 44, 50, 52, 182, 242, 284, 528, 868, 5246, 8473, 8784, 48503, 48509, 146065, 438122, 591216, 1312724, 4325171, 6629045, 6823284, 56075700, 154392832, 248932942, 251237694, 1913253200, 3123337916, 3180792660

Offset: 1

Andrey V. Kulsha, Nov 19 2011

nonn

Heuristics show that these terms are valid, but a strict proof is yet to be done.

Andrey V. Kulsha, Table of n, a(n) for n = 1..48

Cf. A199407, A200567.

cp's OEIS Frontend

A193948 Integers k such that for all i > k the largest prime factor of i(i+1)(i+2)(i+3)(i+4)(i+5)(i+6) exceeds the largest prime factor of k(k+1)(k+2)(k+3)(k+4)(k+5)(k+6).

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