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

1,1

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

Links

Table of n, a(n) for n=1..4.

Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles & Problems connection.

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A046035, A099077, A099078, A099079.

Sequence in context: A356785 A015169 A041953 * A132532 A108023 A365289

Adjacent sequences: A099077 A099078 A099079 * A099081 A099082 A099083

Keyword

base,more,nonn

Author

Farideh Firoozbakht, Oct 23 2004

Status

approved