1,4,9,61,52,___ - Math Central

HOME

Math Central

Quandaries & Queries

Question from Mubashir, a student:

1,4,9,61,,52,___,84,___,18,1,121,___
please tell me its formula and also that rule that is being applied here like adding 3 or subtracting 5 etc.

Using the encyclopedia of integer sequences: https://oeis.org/
the answer is the strange process of: Writing the squares of numbers in order then reversing the digits:

So without reversal it would have been 1,4,9,16,25,36,49,64,81,100,121, ….
Reversing almost leads to your sequence. Is there a typo for the 84 (should be 94) …

Walter

Math Central is supported by the University of Regina and the Imperial Oil Foundation.