A048553
a(n+1) is next smallest prime beginning with a(n), initial prime is 11.
Original entry on oeis.org
11, 113, 11311, 113111, 1131113, 11311133, 1131113353, 113111335313, 11311133531339, 113111335313399, 1131113353133993, 113111335313399321, 11311133531339932153, 1131113353133993215379, 113111335313399321537911
Offset: 0
-
f:= proc(n)
local p, d;
for d from 1 do
p:= nextprime(n*10^d);
if p < (n+1)*10^d then return p fi
od
end proc:
A[1]:= 11:
for n from 2 to 20 do A[n]:= f(A[n-1]) od:
seq(A[n], n=1..20); # Robert Israel, Aug 16 2015
-
a = {11}; Do[k = 1; w = IntegerDigits[a[[n - 1]]];
While[CompositeQ@ FromDigits[Join[w, IntegerDigits@ k]], k += 2];
AppendTo[a, FromDigits[Join[w, IntegerDigits@ k]]], {n, 2, 15}]; a (* Michael De Vlieger, Sep 21 2015 *)
A261269
Minimal prime concatenation sequence with base 2 and seed 11.
Original entry on oeis.org
11, 111, 11101, 111011, 11101111, 111011111, 111011111001, 111011111001111, 1110111110011111, 11101111100111110101, 1110111110011111010101, 11101111100111110101010101, 11101111100111110101010101011, 1110111110011111010101010101111
Offset: 1
In base 2, the least prime starting with seed 1 is 11; the least prime starting with 11 is 111; the least prime starting with 111 is 11101. Triangular format:
11
111
11101
111011
11101111
1110111111
111011111001
-
b = 2; s = {{1}};
Do[NestWhile[# + 1 &, 0, ! (PrimeQ[FromDigits[tmp = Join[Last[s], (nn = #; IntegerDigits[nn - Sum[b^n, {n, l = NestWhile[# + 1 &, 1, ! (nn - (Sum[b^n, {n, #}]) < 0) &] - 1}], b, l + 1])], b]]) &];
AppendTo[s, tmp], {30}]; Map[FromDigits, s]
Map[FromDigits, s] (* A261269 *)
Map[FromDigits[#, b] &, s] (* A261270 *)
(* Peter J. C. Moses, Aug 06 2015 *)
Showing 1-2 of 2 results.