A261310 a(n+1) = abs(a(n) - gcd(a(n), 10n+9)), a(1) = 1.

1, 0, 29, 28, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 269, 268, 267, 266, 265, 264, 263, 262, 261, 260, 259, 258, 257, 256, 255, 254, 253, 252, 251, 250, 249, 248, 247, 246, 245, 244, 243, 242, 241, 240, 239, 238, 237, 236, 235, 234, 233, 232, 231, 230, 229

Offset

1,3

Comments

The absolute value is relevant only when a(n) = 0 in which case a(n+1) = gcd(a(n),10n+9) = 10n+9.

It is conjectured that for all n, a(n) = 0 implies that a(n+1) = 10n+9 is prime, cf. A186263.

Links

Table of n, a(n) for n=1..67.

Example

a(2) = a(1) - gcd(a(1),10+9) = 1 - 1 = 0.
a(3) = |a(2) - gcd(a(2),10*2+9)| = gcd(0,29) = 29 is prime.
a(4) = 28 and 10*4+9 = 49, thus a(5) = 28 - gcd(28,49) = 28 - 7 = 21. Note that for n = 4+32, 10n+9 = 329 is divisible by 7, but for n = 5+21 = 26, 10n+9 = 269 = a(27) is prime. Also, for n = 27+269 = 296, 10n+9 = 2969 = a(297) is prime again.

Prog

(PARI) print1(a=1); for(n=1, 99, print1(", ", a=abs(a-gcd(a, 10*n+9))))

Crossrefs

Cf. A261301 - A261309; A186253 - A186263.

Sequence in context: A303615 A291492 A256441 * A022985 A023471 A070658

Adjacent sequences: A261307 A261308 A261309 * A261311 A261312 A261313

Keyword

nonn

Author

M. F. Hasler, Aug 14 2015

Status

approved