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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

Table of n, a(n) for n=1..12.

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

Adjacent sequences:  A118502 A118503 A118504 * A118506 A118507 A118508

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 November 21 04:33 EST 2019. Contains 329350 sequences. (Running on oeis4.)