

A309521


The sequence is always extended by subtracting the nth digit of the sequence from a(n) if a(n) is prime, else adding it to a(n), starting with a(1) = 4.


3



4, 8, 16, 17, 11, 10, 17, 16, 17, 16, 16, 17, 10, 11, 5, 4, 11, 10, 16, 17, 11, 10, 17, 16, 16, 17, 16, 21, 25, 26, 27, 28, 28, 29, 23, 22, 29, 28, 29, 28, 28, 29, 22, 23, 17, 16, 22, 23, 16, 17, 11, 9, 10, 12, 17, 15, 21, 23, 16, 18, 26, 28, 36, 38, 47, 45
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OFFSET

1,1


COMMENTS

Up to 10^6 the terms increase approximately linearly, and no cycles are visible. As we approach a million terms the terms are 3590238, 3590240, 3590242, 3590248, 3590251, 3590251, 3590257, 3590259, 3590261, 3590267, 3590270, 3590279, 3590285, 3590287, 3590289, 3590295, 3590298, 3590306, 3590312, 3590314, 3590316, 3590322, 3590326, 3590326, 3590332, 3590334, 3590336, 3590342, 3590346, ..., and the smallest values not yet encountered at that point are 2, 3, 6, 7, 13, 14, 19, 20, 24, 30, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 46, 49, 51, 53, 55, 56, 57, 58, 59, 60, 61, 66, 67, 68, 69, 70, 75, 76, 77, 78, 79, 80, 81, 83, 85, 86, 87, 88, 89, 90, 91, 92, 100, 108, 109, 110, 113, 114, 115, 116, 117, 118, ...  Lars Blomberg, Aug 06 2019


LINKS



EXAMPLE

The sequence starts with 4,8,16,17,11,10,17,16,...
As a(1) = 4 (not a prime), we have a(2) = a(1) + [the 1st digit of the seq] = 4 + 4 = 8;
as a(2) = 8 (not a prime), we have a(3) = a(2) + [the 2nd digit of the seq] = 8 + 8 = 16;
as a(3) = 16 (not a prime), we have a(4) = a(3) + [the 3rd digit of the seq] = 16 + 1 = 17;
as a(4) = 17 (a prime), we have a(5) = a(4)  [the 4th digit of the seq] = 17  6 = 11;
as a(5) = 11 (a prime), we have a(6) = a(5)  [the 5th digit of the seq] = 11  1 = 10;
etc.


PROG

(PARI) v=4; d=[]; for (n=1, 66, print1 (v ", "); d=concat(d, digits(v)); v+=d[n]*if (isprime(v), 1, +1)) \\ Rémy Sigrist, Aug 06 2019


CROSSREFS

Cf. A309529 (same idea, but dealing with even numbers instead of primes).


KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



