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A118505 Sophie Germain primes for which the product of the digits is also a Sophie Germain prime. 1
2, 3, 5, 113, 131, 1511, 111111113, 1111111121, 1111111111111111111111111111111121, 111111111111111111111111111111111111131, 111111111113111111111111111111111111111, 111111131111111111111111111111111111111111111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
None of the numbers in the sequence can have digits 0,4,6,7,8 or 9. Either the digits are all 1's, or there is one digit 2,3 or 5 and all the others are 1's.
Comment from Hans Havermann, May 13 2006: If we express these numbers more compactly as (10^x-1)/9 + y*10^z, with y restricted to one of {1,2,4}, then the first 26 values (x < 2010) of {x,y,z} are: {1, 1, 0}, {1, 2, 0}, {1, 4, 0}, {3, 2, 0}, {3, 2, 1}, {4, 4, 2}, {9, 2, 0}, {10, 1, 1}, {34, 1, 1}, {39, 2, 1}, {39, 2, 27}, {57, 2, 49}, {82, 1, 39}, {114, 2, 84}, {129, 2, 69}, {142, 1, 132}, {148, 4, 119}, {148, 4, 132}, {160, 4, 53}, {160, 1, 105}, {244, 1, 16}, {280, 1, 210}, {976, 1, 285}, {1111, 1, 1000}, {1170, 2, 1094}, {1807, 1, 1308}.
The next term has 82 digits. - Harvey P. Dale, Jul 30 2019
LINKS
EXAMPLE
131 is in the sequence because (1) it is a Sophie Germain prime and (2) the product of its digits 1*3*1=3 is also a Sophie Germain prime.
MATHEMATICA
Select[FromDigits/@(Flatten[Permutations/@Flatten[Table[PadRight[{n}, k, 1], {n, {1, 2, 3, 5}}, {k, 60}], 1], 1]), AllTrue[ {#, 2#+1, Times@@ IntegerDigits[ #], 2Times@@ IntegerDigits[ #]+ 1}, PrimeQ]&]//Sort (* Harvey P. Dale, Jul 30 2019 *)
CROSSREFS
Cf. A005384.
Sequence in context: A065406 A111331 A205668 * A067799 A321362 A230372
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), May 06 2006
EXTENSIONS
More terms from Hans Havermann, May 07 2006
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)