A388850 - OEIS

A388850

Initial term of first maximal bad interval of width n, i.e., initial term of the first run of exactly n+1 consecutive integers in A388654; or 0 if no such interval exists.

4, 8, 48, 1680, 76725, 332925, 7474752, 4541154, 75047565

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OFFSET

0,1

COMMENTS

See A388654 for the definition of bad interval.

0 < a(13) <= 17952448643078. (See comment by user StijnC on the Erdős Problems link.)

From Touch Sungkawichai, Jan 03 2026: (Start)

0 < a(9) <= 4928180396.

0 < a(10) <= 40533366231.

0 < a(11) <= 111460496439.

0 < a(12) <= 436502026483. (End)

LINKS

Table of n, a(n) for n=0..8.

Thomas Bloom, Problem 382, Erdős Problems.

Erdős problems database contributors, Erdős problem database, see no. 382.

EXAMPLE

For n = 6, the largest prime factor of the product 7474752*...*7474758 is p = 1367, and the product is divisible by p^2. It is not possible to keep this property if the interval is extended and no earlier interval works (and is maximal), so a(6) = 7474752. (The interval 4541155, ..., 4541161 also works, but is extendable to 4541154, ..., 4541161, giving a(7) = 4541154.)

CROSSREFS

Cf. A388654.

Sequence in context: A045882 A051681 A267987 * A056407 A329942 A056397

Adjacent sequences: A388847 A388848 A388849 * A388851 A388852 A388853

KEYWORD

nonn,hard,more,changed

AUTHOR

Pontus von Brömssen, Sep 21 2025

STATUS

approved