Sequence 1, 3, 7, 12
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 Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics.