A046258 a(1) = 8; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

8, 9, 23, 51, 69, 81, 93, 129, 169, 179, 181, 273, 321, 321, 449, 639, 769, 857, 1047, 1213, 1233, 1443, 1587, 1637, 1953, 2433, 2599, 2639, 2901, 3261, 3681, 4059, 5109, 5169, 5407, 5691, 6149, 6531, 7939, 8081, 8211, 8439, 8589, 8623, 8663, 8757, 9459

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A069610, A074344, A033680, A033679, A033681, A046254, A046255, A046256, A046257, A046259, A111524.

Programs

Maple

A[1]:= 8: A[2]:= 9: x:= 89:
for n from 3 to 100 do
  for y from A[n-1] by 2 do
    z:= x*10^(1+ilog10(y))+y;
    if isprime(z) then break fi;
  od:
  A[n]:= y;
  x:= z;
od:
seq(A[i],i=1..100); # Robert Israel, May 30 2018

Mathematica

a[1] = 8; a[n_] := a[n] = Block[{k = a[n - 1], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k ++ ]; k]; Table[ a[n], {n, 47}] (* Robert G. Wilson v, Aug 05 2005 *)
nxt[{jp_,a_}]:=Module[{k=a},While[CompositeQ[jp 10^IntegerLength[k]+k],k++];{jp 10^IntegerLength[k]+ k,k}]; NestList[nxt,{8,8},50][[;;,2]] (* Harvey P. Dale, Apr 10 2024 *)