A072807 n-th prime prime(n) written in base (prime(n) (mod prime(n-1))).
111, 101, 111, 23, 1101, 101, 10011, 113, 45, 11111, 101, 221, 101011, 233, 125, 135, 111101, 151, 1013, 1001001, 211, 1103, 225, 141, 1211, 1100111, 1223, 1101101, 1301, 91, 2003, 345, 10001011, 149, 10010111, 421, 431, 2213, 445, 455, 10110101
Offset: 2
Examples
Eventually non-decimal digit symbols appear, as in case of 307=17d, in base 14 = 307 mod 293.
Links
- Alois P. Heinz, Table of n, a(n) for n = 2..62 (a(63) needs digits > 9)
Programs
-
Maple
a:= proc(n) local b, p, l; p:= ithprime(n); b:= irem(p, prevprime(p)); if b=1 then l:= 1$p else l:= ""; while p>0 do l:= irem(p, b, 'p'), l od fi; parse(cat(l)) end: seq(a(n), n=2..62); # Alois P. Heinz, Sep 05 2019 -
Mathematica
Table[BaseForm[Prime[w], Mod[Prime[w], Prime[w-1]]], {w, 2, 128}] Join[{111},FromDigits[IntegerDigits[#[[2]],Mod[#[[2]],#[[1]]]]]&/@ Partition[ Prime[Range[2,50]],2,1]] (* Harvey P. Dale, Jul 03 2021 *) -
PARI
a(n) = {my(p=prime(n), q=prime(n-1)); if ((p % q) != 1, d=digits(p, p % q); if (#select(x->(x>9), d), 0, fromdigits(d, 10)), fromdigits(vector(p, k, 1), 10));} \\ Michel Marcus, Sep 05 2019
Extensions
Name corrected by Michel Marcus, Sep 05 2019