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

2,1

Links

Alois P. Heinz, Table of n, a(n) for n = 2..62 (a(63) needs digits > 9)

Example

Eventually non-decimal digit symbols appear, as in case of 307=17d, in base 14 = 307 mod 293.

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 *)

Prog

(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

Crossrefs

Cf. A008713, A072803, A072804, A072805, A072806.

Sequence in context: A282796 A282800 A351320 * A282976 A284083 A252724

Adjacent sequences: A072804 A072805 A072806 * A072808 A072809 A072810

Keyword

nonn,base

Author

Labos Elemer, Jul 12 2002

Extensions

Name corrected by Michel Marcus, Sep 05 2019

Status

approved