A309521 The sequence is always extended by subtracting the n-th digit of the sequence from a(n) if a(n) is prime, else adding it to a(n), starting with a(1) = 4.

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

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

Lars Blomberg, Table of n, a(n) for n = 1..10000

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).

Sequence in context: A166634 A189007 A242349 * A072603 A123535 A312765

Adjacent sequences: A309518 A309519 A309520 * A309522 A309523 A309524

Keyword

base,nonn

Author

Eric Angelini and Lars Blomberg, Aug 06 2019

Extensions

More terms from Rémy Sigrist, Aug 06 2019

Status

approved