A069602 a(1) = 1; a(n) = smallest composite number such that the juxtaposition a(1)a(2)...a(n) is a prime.

1, 9, 9, 9, 21, 9, 51, 21, 9, 57, 301, 51, 51, 33, 209, 111, 87, 153, 121, 87, 63, 39, 77, 27, 57, 81, 129, 147, 111, 21, 147, 321, 69, 93, 153, 621, 817, 129, 81, 803, 129, 153, 451, 171, 717, 801, 959, 459, 187, 291, 231, 533, 399, 291, 289, 869, 489, 171, 381, 667, 21

Offset: 1

Author

Amarnath Murthy, Mar 26 2002

Keywords

• nonn
• base

Examples

			a(5) = 21 and the number 199921 is a prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A033680, A074336, A092528.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{k = 3, c = IntegerDigits @ Table[ a[i], {i, n - 1}]}, While[PrimeQ[k] || !PrimeQ[FromDigits @ Flatten @ Append[c, IntegerDigits[k]]], k += 2]; k]; Table[ a[n], {n, 61}] (* Robert G. Wilson v, Aug 05 2005 *)
nxt[{jx_,a_}]:=Module[{c=9},While[PrimeQ[c]||CompositeQ[jx*10^IntegerLength[c]+c],c+=2];{jx*10^IntegerLength[c]+c,c}]; NestList[nxt,{1,1},60][[;;,2]] (* Harvey P. Dale, Feb 08 2025 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 31 2003