A186256 -id:A186256 - cp's OEIS frontend

A261304 a(n+1) = abs(a(n) - gcd(a(n), 4n+3)), a(1) = 1.

1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 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, 251, 250, 249, 248, 247, 246, 245, 244, 243, 242, 241, 240, 239, 238, 237, 236

Offset: 1

M. F. Hasler, Aug 14 2015

nonn

The absolute value is relevant only when a(n) = 0, in which case a(n+1) = gcd(a(n), 4n+3) = 4n+3.

It is conjectured that a(n) = 0 implies that 4n+3 = a(n+1) is prime, cf. A186256. (This is the sequence {u(n)} mentioned there.)

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

print1(a=1);for(n=1,199,print1(",",a=abs(a-gcd(a,4*n+3))))

A261305 a(n+1) = abs(a(n) - gcd(a(n), 5*n+4)), u(1) = 1.

Original entry on oeis.org

1, 0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 89, 88, 77, 76, 75, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 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

Offset: 1

M. F. Hasler, Aug 14 2015

nonn

It is conjectured that a(n) = 0 implies that 5n+4 = a(n+1) is prime for n > 2, cf. A186256. (This is the sequence {u(n)} mentioned there.)

			a(2) = a(1) - gcd(a(1),5+4) = 1 - 1 = 0.
a(3) = |a(2) - gcd(a(2),5*2+4)| = 14.
a(19) = 88, thus a(20) = 88 - gcd(88, 5*19+4) = 88 - 11 = 77.

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

print1(a=1);for(n=1,199,print1(",",a=abs(a-gcd(a,5*n+4))))

cp's OEIS Frontend

A261304 a(n+1) = abs(a(n) - gcd(a(n), 4n+3)), a(1) = 1.

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