A261306 a(n+1) = abs((n) - gcd(a(n), 6*n+5)), a(1) = 1.

1, 0, 17, 16, 15, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 101, 100, 99, 98, 97, 96, 95, 94, 93, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 461, 460, 459, 458, 457, 456

Offset

1,3

Comments

It is conjectured that for all n, a(n) = 0 implies that a(n+1) = 6n+5 is prime, cf. A186258. (This is the sequence {u(n)} mentioned there.)

Links

Table of n, a(n) for n=1..82.

Example

a(2) = a(1) - gcd(a(1),6+5) = 1 - 1 = 0.
a(3) = |a(2) - gcd(a(2),6*2+5)| = gcd(0,17) = 17 is prime.
a(5) = 15, thus a(6) = 15 - gcd(15,6*5+5) = 15 - 5 = 10; similarly after a(25) = 93.

Prog

(PARI) print1(a=1); for(n=1, 199, print1(", ", a=abs(a-gcd(a, 6*n+5))))

Crossrefs

Cf. A261301 - A261310, A186253 - A186263, A106108.

Sequence in context: A004506 A096181 A248941 * A022973 A023459 A004458

Adjacent sequences: A261303 A261304 A261305 * A261307 A261308 A261309

Keyword

nonn

Author

M. F. Hasler, Aug 14 2015

Status

approved