A074342 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, 19, 21, 23, 27, 57, 183, 207, 231, 247, 267, 399, 417, 441, 459, 569, 603, 693, 847, 933, 1107, 1149, 1197, 1251, 1581, 1619, 2061, 2137, 2139, 2339, 2643, 2703, 2743, 2847, 2987, 3199, 3447, 3477, 3641, 3919, 4241, 4369, 4599, 4761, 6647, 6739, 6831

Offset: 1

Author

Zak Seidov, Sep 23 2002

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..439

Crossrefs

Cf. A046256, A069608, A074336, A074338, A074339, A074340, A074341, A074343, A074344, A074345, A074346.

Programs

Mathematica

a[1] = 6; a[n_] := a[n] = Block[{k = a[n - 1] + 1 + Mod[a[n - 1], 2], c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[ !PrimeQ[ FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 48}] (* Robert G. Wilson v *)
nxt[{j_,a_}]:=Module[{k=a+2},While[CompositeQ[j(10^ IntegerLength[ k])+k],k+=2];{j(10^IntegerLength[k])+k,k}]; Join[{6},NestList[ nxt,{67,7},50][[All,2]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 19 2021 *)

Python

from sympy import isprime
def aupton(terms):
  alst, astr = [6], "6"
  for n in range(2, terms+1):
    an = alst[-1] + 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

Extensions

Corrected and extended by Robert G. Wilson v, Aug 05 2005