A099080 Numbers k such that sigma(k).sigma(k-1) ... sigma(2).sigma(1) is prime (dot between numbers means concatenation).

2, 3, 66, 102

Offset: 1

Author

Farideh Firoozbakht, Oct 23 2004

Keywords

• base
• more
• nonn

Comments

Numbers of digits of primes corresponding to the four known terms of this sequence are respectively 2, 3, 133, and 232.

A naive heuristic suggests that this sequence is infinite but extremely sparse. - Charles R Greathouse IV, Nov 05 2013

There are no more terms below 10000. - Charles R Greathouse IV, Nov 09 2013

There are no more terms below 20000. - Michael S. Branicky, Nov 25 2024

Examples

			3 is in the sequence because sigma(3).sigma(2).sigma(1) = 431 is prime.
		

Links

• Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles & Problems connection.
• Eric Weisstein's World of Mathematics, Integer Sequence Primes

Crossrefs

Cf. A046035, A099077, A099078, A099079.

Programs

Mathematica

Module[{nn=110,d},d=DivisorSigma[1,Range[nn]];Select[Range[nn], PrimeQ[ FromDigits[ Flatten[IntegerDigits/@Reverse[Take[d,#]]]]]&]] (* Harvey P. Dale, Jul 25 2016 *)

PARI

s="1";for(n=2,1e3,s=Str(sigma(n),s);if(ispseudoprime(eval(s)), print1(n", "))) \\ Charles R Greathouse IV, Nov 05 2013