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A conjectured permutation (proof?) of the nonnegative composite numbers interleaved with the sequence of primes


---------- Forwarded message ----------
From: Eric Angelini <Eric.Angelini@kntv.be>
To: Sequence Fanatics Discussion list <seqfan@list.seqfan.eu>
Cc: 
Date: Mon, 14 Jan 2013 18:19:53 +0100
Subject: [seqfan] Primes and prime sums
Hello Seq-Fans,

Write down the prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, ...

Insert between two primes the
smallest integer not yet present
in the sequence such that two
neighboring integers sum up to
a prime.

I think the sequence starts:
2,0,3,8,5,6,7,12,11,18,13,26,17,...
Best,
É.

I added a mention of your interesting idea in:

Permutation of the nonnegative integers#A conjectured permutation (proof?) of the nonnegative composite numbers interleaved with the sequence of primes

This is possibly a permutation of zero and the nonnegative composite numbers (proof?) interleaved with the sequence of primes, thus possibly a permutation of the nonnegative integers, except for the unit 1 which is not included.

If you considered:

Write down the [positive] odd noncomposites:

{1, 3, 5, 7, 11, 13, 17, 19, 23, ...}

Insert between two [positive] odd noncomposites the smallest [positive] integer not yet present in the sequence such that two neighboring integers sum up to a prime.

You'd possibly get a permutation of the positive integers (proof?):

{1, 2, 3, 8, 5, 6, 7, 12, 11, 18, 13, 26, 17, ...}

In either case, those are interesting sequences, and also the sequences of interleaved composite numbers. — Daniel Forgues 21:23, 20 January 2013 (UTC)

Oops, the odd composites can't obviously be there. I really fumbled there... I'd really appreciate if you removed that part... (Since this is your talk page, only you can decide that...) — Daniel Forgues 03:17, 21 January 2013 (UTC)

A conjectured permutation (proof?) of the primes interleaved with the sequence of nonprime numbers


---------- Forwarded message ----------
From: Eric Angelini <Eric.Angelini@kntv.be>
To: Sequence Fanatics Discussion list <seqfan@list.seqfan.eu>
Cc: Alexandre Wajnberg <alexandre.wajnberg@skynet.be>
Date: Tue, 15 Jan 2013 11:49:33 +0100
Subject: [seqfan] Non-primes and non-prime sums
Hello Seq-Fans,

Write down the non prime numbers:

1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ...

Insert between two non-primes the
smallest prime not yet present
in the sequence such that two
neighboring integers sum to a
non-prime.

I think the sequence starts:

1,5,4,2,6,43,8,7,9,11,10,23,12,13,14,31,15,17,16,...

Best,
É.

I added a mention of your interesting idea in:

Permutation of the positive integers#A conjectured permutation (proof?) of the primes interleaved with the sequence of nonprime numbers

I hope I'm not fumbling this time! — Daniel Forgues 03:17, 21 January 2013 (UTC)

Towards an index of your SeqFan/OEIS contributions

Hello Eric (and anyone who comes to read this page),

I think it would be time (but I don't have that much...) to make an index of your contributions, maybe using some classifications like

  • (p) - permutations of the integers
  • (b) - based on digits in base 10 (or another base)
  • (d) - based on divisibility (not mutually exclusive with (d)...)
  • (s) - self describing
  • (s')- not self describing (if any?)

but I don't know what would be the most relevant such "categorization" or any other/better idea to start such a list... MFH 02:19, 30 September 2014 (UTC)

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