[seqfan] Re: Silent numbers

Wed Nov 29 13:39:39 CET 2023

I like the idea.  It has two things going on with both the silent evens, and the "handing over amounts" after starting with an initial amount plus what was handed to each number.  If I understand correctly, it's the amount that is handed over that Ali wants in the sequence, not the amount each number keeps.  (I imagine the amount kept would be a good companion sequence.)

 I wrote some Python code to generate the terms, at least as I understand them.

def silent_evens(n):
        digits = [int(i) for i in str(n)]
        end = int(digits[-1])
        return end if len(digits) in {1, 2} else silent_evens(n // 100)*10 + end

def amount_handed(n):
        return 1 if n==1 else silent_evens(n + amount_handed(n-1))

This gives us this for the first thousand terms:

1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 11, 15, 10, 16, 13, 11, 10, 10, 11, 13, 16, 10, 15, 11, 18, 16, 15, 15, 16, 18, 11, 15, 10, 16, 13, 11, 10, 10, 11, 13, 16, 10, 15, 11, 18, 16, 15, 15, 16, 18, 11, 15, 10, 16, 13, 11, 10, 10, 11, 13, 16, 10, 15, 11, 18, 16, 15, 15, 16, 18, 11, 15, 10, 16, 13, 11, 10, 10, 11, 13, 16, 10, 15, 11, 18, 16, 15, 15, 16, 18, 11, 15, 10, 16, 13, 11, 10, 10, 11, 13, 16, 20, 25, 21, 28, 26, 25, 25, 26, 28, 21, 25, 20, 26, 23, 21, 20, 20, 21, 23, 26, 20, 25, 21, 28, 26, 25, 25, 26, 28, 21, 25, 20, 26, 23, 21, 20, 20, 21, 23, 26, 20, 25, 21, 28, 26, 25, 25, 26, 28, 21, 25, 20, 26, 23, 21, 20, 20, 21, 23, 26, 20, 25, 21, 28, 26, 25, 25, 26, 28, 21, 25, 20, 26, 23, 21, 20, 20, 21, 23, 26, 20, 25, 21, 28, 26, 25, 25, 26, 28, 31, 35, 30, 36, 33, 31, 30, 30, 31, 33, 36, 30, 35, 31, 38, 36, 35, 35, 36, 38, 31, 35, 30, 36, 33, 31, 30, 30, 31, 33, 36, 30, 35, 31, 38, 36, 35, 35, 36, 38, 31, 35, 30, 36, 33, 31, 30, 30, 31, 33, 36, 30, 35, 31, 38, 36, 35, 35, 36, 38, 31, 35, 30, 36, 33, 31, 30, 30, 31, 33, 36, 30, 35, 31, 38, 36, 35, 35, 36, 38, 31, 35, 30, 36, 33, 31, 30, 30, 31, 33, 36, 40, 45, 41, 48, 46, 45, 45, 46, 48, 41, 45, 40, 46, 43, 41, 40, 40, 41, 43, 46, 40, 45, 41, 48, 46, 45, 45, 46, 48, 41, 45, 40, 46, 43, 41, 40, 40, 41, 43, 46, 40, 45, 41, 48, 46, 45, 45, 46, 48, 41, 45, 40, 46, 43, 41, 40, 40, 41, 43, 46, 40, 45, 41, 48, 46, 45, 45, 46, 48, 41, 45, 40, 46, 43, 41, 40, 40, 41, 43, 46, 40, 45, 41, 48, 46, 45, 45, 46, 48, 51, 55, 50, 56, 53, 51, 50, 50, 51, 53, 56, 50, 55, 51, 58, 56, 55, 55, 56, 58, 51, 55, 50, 56, 53, 51, 50, 50, 51, 53, 56, 50, 55, 51, 58, 56, 55, 55, 56, 58, 51, 55, 50, 56, 53, 51, 50, 50, 51, 53, 56, 50, 55, 51, 58, 56, 55, 55, 56, 58, 51, 55, 50, 56, 53, 51, 50, 50, 51, 53, 56, 50, 55, 51, 58, 56, 55, 55, 56, 58, 51, 55, 50, 56, 53, 51, 50, 50, 51, 53, 56, 60, 65, 61, 68, 66, 65, 65, 66, 68, 61, 65, 60, 66, 63, 61, 60, 60, 61, 63, 66, 60, 65, 61, 68, 66, 65, 65, 66, 68, 61, 65, 60, 66, 63, 61, 60, 60, 61, 63, 66, 60, 65, 61, 68, 66, 65, 65, 66, 68, 61, 65, 60, 66, 63, 61, 60, 60, 61, 63, 66, 60, 65, 61, 68, 66, 65, 65, 66, 68, 61, 65, 60, 66, 63, 61, 60, 60, 61, 63, 66, 60, 65, 61, 68, 66, 65, 65, 66, 68, 71, 75, 70, 76, 73, 71, 70, 70, 71, 73, 76, 70, 75, 71, 78, 76, 75, 75, 76, 78, 71, 75, 70, 76, 73, 71, 70, 70, 71, 73, 76, 70, 75, 71, 78, 76, 75, 75, 76, 78, 71, 75, 70, 76, 73, 71, 70, 70, 71, 73, 76, 70, 75, 71, 78, 76, 75, 75, 76, 78, 71, 75, 70, 76, 73, 71, 70, 70, 71, 73, 76, 70, 75, 71, 78, 76, 75, 75, 76, 78, 71, 75, 70, 76, 73, 71, 70, 70, 71, 73, 76, 80, 85, 81, 88, 86, 85, 85, 86, 88, 81, 85, 80, 86, 83, 81, 80, 80, 81, 83, 86, 80, 85, 81, 88, 86, 85, 85, 86, 88, 81, 85, 80, 86, 83, 81, 80, 80, 81, 83, 86, 80, 85, 81, 88, 86, 85, 85, 86, 88, 81, 85, 80, 86, 83, 81, 80, 80, 81, 83, 86, 80, 85, 81, 88, 86, 85, 85, 86, 88, 81, 85, 80, 86, 83, 81, 80, 80, 81, 83, 86, 80, 85, 81, 88, 86, 85, 85, 86, 88, 91, 95, 90, 96, 93, 91, 90, 90, 91, 93, 96, 90, 95, 91, 98, 96, 95, 95, 96, 98, 91, 95, 90, 96, 93, 91, 90, 90, 91, 93, 96, 90, 95, 91, 98, 96, 95, 95, 96, 98, 91, 95, 90, 96, 93, 91, 90, 90, 91, 93, 96, 90, 95, 91, 98, 96, 95, 95, 96, 98, 91, 95, 90, 96, 93, 91, 90, 90, 91, 93, 96, 90, 95, 91, 98, 96, 95, 95, 96, 98, 91, 95, 90, 96, 93, 91, 90, 90, 91, 93, 96, 0, 95, 1, 98, 6, 95, 5, 96, 8, 91, 5, 90, 6, 93, 1, 90, 0, 91, 3, 96, 0, 95, 1, 98, 6, 95, 5, 96, 8, 91, 5, 90, 6, 93, 1, 90, 0, 91, 3, 96, 0, 95, 1, 98, 6, 95, 5, 96, 8, 91, 5, 90, 6, 93, 1, 90, 0, 91, 3, 96, 0, 95, 1, 98, 6, 95, 5, 96, 8, 91, 5, 90, 6, 93, 1, 90, 0, 91, 3, 96, 0, 95, 1, 98, 6, 95, 5, 96, 8, 1, 95, 0, 96, 3, 1, 0, 0

-David

-----Original Message-----
From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of Ali Sada via SeqFan
Sent: Wednesday, November 22, 2023 1:02 AM
To: Sequence Fanatics Discussion List <seqfan at list.seqfan.eu>
Cc: Ali Sada <pemd70 at yahoo.com>
Subject: [seqfan] Silent numbers

Hi everyone,
Finnish comedian, ISMO, doesn't like silent letters in English words. He thinks that silent numbers are far more useful, "like I owe you 75 dollars, but the 7 is silent."

Let's say that each positive integer, n, has n dollars. But n owes money to n+1 and it has to give that money back. However, in this world, the even-numbered digits are "silent." For example, 152 becomes 12, and 7643 becomes 63, and so on.

We start:

1 has one dollar and it gives it to 2. a(1) =1.
2 has 3 dollars now and it gives them to 3. a(2) = 3.3 has 6 dollars now and it gives them to 4. a(3) = 6.4 has 10 dollars now, but it gives 0 to 5 since the 1 is silent. a(4) = 0.5 has 5 dollars and it gives them to 6. a(5) = 5.
And so on.
Is this sequence suitable for the OEIS?

Best,
Ali
https://www.youtube.com/watch?v=hE38Bq3WArg&t=40s

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