# [seqfan] Re: Insert a "plus" sign to produce a prime

Eric Angelini Eric.Angelini at kntv.be
Fri Nov 14 16:44:56 CET 2014

```Yes, Felix, pardon me for the bad definition -- I had in mind that an
integer belonging to the sequence
produces at least one prime; your
example with 121 illustrates that:
121 belongs to A because 12+1=13.
We do not care here that 1+21 doesn't
produce a prime. But you're right,
an A' sequence where all possible
insertions produce a prime would
be of interest...
Best,
É.
Catapulté de mon aPhone

> Le 14 nov. 2014 à 13:36, "Felix Fröhlich" <felix.froe at googlemail.com> a écrit :
>
> Hi Eric,
>
> This is a nice sequence I think. Is the definition such that at least one
> such prime must exist or do all numbers produced by all possible plus sign
> insertions have to be prime. I assume the former, since in the case of 121,
> 1+21=22 is not prime. Maybe the definition could be made a bit more precise.
>
> Best,
>
> Felix
>
> 2014-11-14 11:32 GMT+01:00 Eric Angelini <Eric.Angelini at kntv.be>:
>
>> Hello Seqfans,
>> Insert a "plus" sign somewhere in a(n): the addition produces a prime.
>>
>> A = 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 49,
>>    50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 101,
>>    103, 107, 109, 110, 112, 116, 118, 121, ...
>>
>> Examples:
>>
>> 11 is in A because 1+1 produces 2, which is prime
>> 12 is in A because 1+2 produces 3, which is prime
>> ...
>> 98 is in A because 9+8 produces 17, which is prime
>> 99 is not in A because 9+9=18 is not prime
>> ...
>> 101 is in A because 10+1 produces 11, which is prime
>> 102 is not in A because 10+2=12 is not prime AND
>>    because 1+02 has no meaning (no leading zeros
>>    admitted, nowhere)
>> Best,
>> É.
>> -----
>> P.-S.
>> The D sequence of primes produced by a "minus" sign starts like this:
>> D = 20, 30, 31, 41, 42, 50, 52, 53, 61, 63, 64, 70, ...
>>
>>
>>
>> _______________________________________________
>>
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>
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>
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```

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