A261308 a(n+1) = abs(a(n) - gcd(a(n), 8n+7)), a(1) = 1.

1, 0, 23, 22, 21, 20, 15, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 167, 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 144, 143, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 132, 131, 130, 129, 128, 127, 126, 125, 124, 123, 122

Offset

1,3

Comments

It is conjectured that for all n, a(n) = 0 implies that 8n+7 = a(n+1) is prime, cf. A186260. (This is the sequence {u(n)} mentioned there.)

Links

Table of n, a(n) for n=1..66.

Example

a(2) = a(1) - gcd(a(1),8+7) = 1 - 1 = 0.
a(3) = |a(2) - gcd(a(2),8*2+7)| = gcd(0,23) = 23 (= A186260(1)) is prime.
a(6) = 20 and 8*6+7 = 55, thus a(7) = 20 - gcd(20,55) = 20 - 5 = 15.
a(8) = 15 - gcd(15,8*7+7) = 15 - 3 = 12. Note that for n = 8 + a(8) = 20, we have that 8n+7 = 167 = a(20+1) = A186260(2) is prime, while for n = 3 + a(3) = 26, 8n+7 = 215 was divisible by 5, and for n = 7 + a(7) = 22, 8n+7 = 183 was divisible by 3.

Prog

(PARI) print1(a=1); for(n=1, 99, print1(", ", a=abs(a-gcd(a, 8*n+7))))

Crossrefs

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

Sequence in context: A077576 A004512 A214342 * A022979 A023465 A004464

Adjacent sequences: A261305 A261306 A261307 * A261309 A261310 A261311

Keyword

nonn

Author

M. F. Hasler, Aug 14 2015

Status

approved