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A309620 Start with a(1) = 5. For n>1, the sequence is always extended with a(n+1) = a(n) + 2*d if d is prime, and with a(n+1) = a(n) - 1 - d if d is not prime, where d is the n-th digit of the sequence. 1
5, 15, 13, 23, 21, 27, 31, 37, 41, 39, 43, 57, 63, 61, 67, 81, 76, 74, 80, 70, 65, 71, 81, 95, 88, 94, 87, 85, 78, 92, 83, 81, 95, 88, 102, 97, 88, 87, 101, 100, 93, 103, 117, 115, 106, 104, 94, 104, 95, 86, 76, 71, 62, 76, 67, 77, 91, 82, 72, 76, 67, 73, 64, 62, 52, 62, 53, 44, 42, 41, 45, 35, 49, 40, 31, 22, 36, 34, 33, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If we start with a positive number less than 5 the sequence enters almost immediately into a 1-term loop.

The authors wanted the sequence to oscillate evenly around zero by giving different weights to the nonprime vs prime digits: 0, 1, 4, 6, 8, 9 have respective weights 1, 2, 5, 7, 9, 10 (total 34) and 2, 3, 5, 7 become 4, 6, 10, 14 (same total 34).

The result is not convincing after 10^5 terms, the sequence staying for almost 95% of the time above zero. But who knows what will happen after 10^10 terms, for instance?

LINKS

Jean-Marc Falcoz, Table of n, a(n) for n = 1..65531

EXAMPLE

The sequence S begins with 5,15,13,23,21,27,31,37,...

As a(1) = 5 and the 1st digit of S is prime (5), we get a(2) = a(1) + 2*5 = 5 + 10 = 15;

as a(2) = 15 and the 2nd digit of S is not prime (1), we get a(3) = a(2) - 1 - 1 = 15 - 2 = 13;

as a(3) = 13 and the 3rd digit of S is prime (5), we get a(4) = a(3) + 2*5 = 13 + 10 = 23;

as a(4) = 23 and the 4th digit of S is not prime (1), we get a(5) = a(4) - 1 - 1 = 23 - 2 = 21;

as a(5) = 21 and the 5th digit of S is prime (3), we get a(6) = a(5) + 2*3 = 21 + 6 = 27;

as a(6) = 27 and the 6th digit of S is prime (2), we get a(7) = a(6) + 2*2 = 27 + 4 = 31;

etc.

CROSSREFS

Cf. A309521 (a variant).

Sequence in context: A302841 A113259 A298265 * A291794 A321775 A166621

Adjacent sequences:  A309617 A309618 A309619 * A309621 A309622 A309623

KEYWORD

base,sign

AUTHOR

Eric Angelini and Jean-Marc Falcoz, Aug 10 2019

STATUS

approved

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Last modified June 14 03:38 EDT 2021. Contains 345018 sequences. (Running on oeis4.)