

A261308


a(n+1) = abs(a(n)  gcd(a(n), 8n+7)), a(1) = 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
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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(agcd(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



