Hi Zak and all

This is pretty cool. On cursory inspection your sequence looks fine.
Personally I found the first sequence more interesting. In the
numbers you provided in the first sequence, a curiousity: if the
digits of a number are added up and have an odd sum then the sum is
prime. So I checked for more of these numbers up to 1,000
(which are 587, 607, 613, 617, 631, 653, 659, 661, 673, 769, 809,
829, 839, 857, 863, 883, 929 and 967) and the rule still holds! But
surely that is too good to be true for long!

While looking at primes with even digits, could it be that
3,5,7,11,13,17,19 is the largest string of consecutive primes with
entirely odd digits?

The numbers 653,659,661 and 673 are consecutive primes which meet the
criteria of your first sequence. I wonder if there is a larger
string of consecutive primes which would be in your sequence. (hehe)


Mark






--- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>
wrote:
>
> 1. These are several first primes with at least one non_zero even
> digit which remain primes after dividing the even digits by two:
>
>
23,29,43,61,67,83,167,223,239,251,257,269,293,367,389,421,433,439,443,
> 449,457,463,541 (A086060?)
>
> From the first 1,000,000 primes, 153043 are such, and the largest
is
> 15485807 -> 15245407.
>
> Are these primes known?
>
> 2. If one looks for "integers with at least one non_zero even
> which become primes after dividing the even digits by two",
>
> here they are (A086059?)
>
>
4,6,12,16,21,22,23,26,27,29,32,43,46,49,56,61,62,67,72,76,81,82,83,86,
> 87,102,106,116,123,126,
>
> From the first 1,000,000 integers, 114266 are such, and the
largest
> is 999962 -> 999931.
>
> Thanks for your comments,
> Zak
>
> PS Learned from my first postings (and many thanks to Mike Oakes,
> and to Mark Underwood) I'll wait for your help before sending these
> sequences to OEIS,
>
> many thanks again,
> Zak