A046256 a(1) = 6; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.

6, 7, 7, 9, 27, 59, 69, 181, 201, 257, 267, 399, 573, 603, 861, 901, 923, 1021, 1133, 1239, 1251, 1519, 1589, 1729, 1863, 1901, 2541, 3001, 3017, 3049, 3243, 4407, 4481, 5457, 5839, 5889, 5919, 6159, 6201, 6293, 6577, 6603, 6969, 7217, 8131, 8981, 9033

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..441 (terms 1..100 from Harvey P. Dale)

Crossrefs

Cf. A069608, A074342, A033680, A033679, A033681, A046254, A046255, A046257, A046258, A046259, A111524.

Programs

Mathematica

a[1] = 6; 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[{j_,a_}]:=Module[{k=a},While[!PrimeQ[j*10^IntegerLength[k]+k], k++];{j*10^IntegerLength[k]+k,k}]; Transpose[NestList[nxt,{6,6},50]][[2]] (* Harvey P. Dale, May 07 2016 *)

Python

from sympy import isprime
def aupton(terms):
  alst, astr = [6], "6"
  for n in range(2, terms+1):
    an = alst[-1]
    while not isprime(int(astr+str(an))): an += 1
    alst, astr = alst + [an], astr + str(an)
  return alst
print(aupton(62)) # Michael S. Branicky, Jun 07 2021