Answer to Question #112784 in Combinatorics | Number Theory for Fuad

Question

What is the next number of this sequence 1,2,6,12,20,29?

Answer 1

Answer: 39

$Let's\;write\;following\;sequence:\\B\;=\;1,4,6,8,9,10,...\\This\;numbers\;are\;sequence\;of\;non-prime\;\\numbers.\\And\;our\;sequence\;A\;=\;1,2,6,12,20,29,x...\;\\has\;following\;rule:\\A_n-A_{n-1}=B_{n-1}\\2-1\;=\;1\;\;\;\;\;\;\;\;\;\;\;\;\;\;6-2\;=\;4\\12-6=6\;\;\;\;\;\;\;\;\;\;\;\;\;20-12=8\\29-20=9\\So,\;x-29=10\Rightarrow\;x=39$