User blog comment:Alemagno12/Rayo and FOST/@comment-27173506-20160331154639

I provided a formula for writing a number n in 42n+8 symbols on vel's talk page:  0 is defined as "¬∃n(n∈a 0 )", and a n+1  is recursively defined as: "... ∧ a n ∈a n+1 ∧¬∃n(n∈a n ∧¬(n∈a n+1 ))∧¬∃n(n∈a n+1 ∧¬(n=a n )∧¬(n∈a n )"

As for reducing the number of symbols: look at the FOST page by vel. You can use the existential symbol, membership symbol and NAND with RPN, but it's slower. Unconnectedly, I'll update the FOST golf page now with some way better bounds.