|
%I #17 Jul 03 2021 15:58:14
%S 111,101,111,23,1101,101,10011,113,45,11111,101,221,101011,233,125,
%T 135,111101,151,1013,1001001,211,1103,225,141,1211,1100111,1223,
%U 1101101,1301,91,2003,345,10001011,149,10010111,421,431,2213,445,455,10110101
%N n-th prime prime(n) written in base (prime(n) (mod prime(n-1))).
%H Alois P. Heinz, <a href="/A072807/b072807.txt">Table of n, a(n) for n = 2..62</a> (a(63) needs digits > 9)
%e Eventually non-decimal digit symbols appear, as in case of 307=17d, in base 14 = 307 mod 293.
%p a:= proc(n) local b, p, l;
%p p:= ithprime(n); b:= irem(p, prevprime(p));
%p if b=1 then l:= 1$p
%p else l:= ""; while p>0 do l:= irem(p, b, 'p'), l od
%p fi; parse(cat(l))
%p end:
%p seq(a(n), n=2..62); # _Alois P. Heinz_, Sep 05 2019
%t Table[BaseForm[Prime[w], Mod[Prime[w], Prime[w-1]]], {w, 2, 128}]
%t Join[{111},FromDigits[IntegerDigits[#[[2]],Mod[#[[2]],#[[1]]]]]&/@ Partition[ Prime[Range[2,50]],2,1]] (* _Harvey P. Dale_, Jul 03 2021 *)
%o (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
%Y Cf. A008713, A072803, A072804, A072805, A072806.
%K nonn,base
%O 2,1
%A _Labos Elemer_, Jul 12 2002
%E Name corrected by _Michel Marcus_, Sep 05 2019
|
