A200065 Start with n, concatenate its trivial divisors, and repeat until a prime is reached. a(n) = 0 if no prime is ever reached.

0, 0, 13, 0, 0, 0, 17, 0, 19, 0, 1111111111111111111, 0, 113, 0, 0, 0, 1117, 0, 11119, 0, 111121, 0, 1123, 0, 0, 0, 127, 0, 1129, 0, 131, 0

Offset: 1

Author

Arkadiusz Wesolowski, Apr 18 2012

Keywords

• base
• nonn

Comments

a(33) has 715 digits and is too large to include.

a(A065502(n)) = 0. There are other integers for which a(n) = 0 (i.e., n = 221).

The number (10^270343 - 1)/9 appears 161046 times in this sequence.

All odd primes from A096497 are in the sequence.

Examples

			17 -> {1, 17} = 117 (composite) -> {1, 117} = 1117 (prime), so a(17) = 1117.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1032

Crossrefs

Cf. A004022, A096497.

Programs

Mathematica

lst = {}; Do[If[DivisorSigma[0, n] == 1 || Divisible[n, 5] || EvenQ[n], AppendTo[lst, 0], If[PrimeQ[n], n = 10^Length[IntegerDigits[n]] + n]; While[True, If[PrimeQ[n], Break[]]; n = FromDigits[Flatten[IntegerDigits[{1, n}]]]]; AppendTo[lst, n]], {n, 32}]; lst