Sequence - Puzzle Prime

Sequence 1, 3, 7, 12

Section: Brain Teasers Category: Insight

Difficulty: Medium Tags: Sequence

Which is the next number in the following sequence:

1, 3, 7, 12, 18, 26, 35, 45, 56, ?

SOLUTION

This is the so called Hofstadter Figure-Figure Sequence.

The sequence of the differences between the consecutive numbers in the original sequence is 2, 4, 5, 6, 8, 9, 10, 11… These are exactly the natural numbers missing from the original sequence. Therefore, the next number should be 56 + 13 = 69.

Douglas Hofstadter October 13, 2022

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FEATURED

Sequence 1, 11, 21, 1112

Section: Brain Teasers Category: Insight

Difficulty: Advanced Tags: Featured, Sequence

What follows next in the following sequence:

1, 11, 21, 1112, 3112, 211213, 312213, ?

SOLUTION

Every term in the sequence describes how many 1s, 2s, 3s, etc. were there in the previous term. “11” means that in the previous term there was one 1. “21” means that in the previous term there were two 1s. “1112” means that in the previous term there were one 1 and one 2. “3112” means that in the previous term there were three 1s and one 2. “211213” means that in the previous term there were two 1s, one 2 and one 3. “312213” means that in the previous term there were three 1s, two 2s and one 3. Therefore, the next number in the sequence should be 212223.