A186261 -id:A186261 - cp's OEIS frontend

A186263 a(n) = 10*b_10(n) + 9, where b_10 lists the indices of zeros of the sequence A261310: u(n) = abs(u(n-1) - gcd(u(n-1), 10n-1)), u(1) = 1.

29, 269, 2969, 32609, 357169, 3928669, 43213789, 475113649, 5226205969, 57488152069, 632360271769, 6955957188049, 76515529068529, 841670819753809, 9258379017291889, 101842168949117209, 1120263858440288929, 12322902442843176229, 135551926871245562989

Offset: 1

Benoit Cloitre, Feb 16 2011

nonn

For any fixed integer m>=1 define u(1)=1 and u(n)=abs(u(n-1)-gcd(u(n-1),m*n-1)). Then (b_m(k))_{k>=1} is the sequence of integers such that u(b_m(k))=0 and we conjecture that for k large enough m*b_m(k)+m-1 is a prime number. Here for m=10 it appears a(n) is prime for n>=1.

See A261310 for the sequence u relevant here (m=10). - M. F. Hasler, Aug 14 2015

Benoit Cloitre, 10 conjectures in additive number theory, preprint arXiv:2011.4274 [math.NT] , 2011.
M. F. Hasler, Rowland-Cloître type prime generating sequences, OEIS Wiki, August 2015.

Cf. A106108.

Cf. A261301 - A261310; A186253 - A186261.

a=1; m=10; for(n=2, 1e7, a=abs(a-gcd(a, m*n-1)); if(a==0, print1(m*n+m-1, ", ")))

m=10; a=k=1; for(n=1, 20, while( a>D=vecmin(apply(p->a%p, factor(N=m*(k+a)+m-1)[, 1])), a-=D+gcd(a-D, N); k+=1+D); k+=a+1; print1(a=N, ", ")) \\ M. F. Hasler, Aug 22 2015

We conjecture that a(n) is asymptotic to c*11^n with c>0.

See the wiki link for a sketch of a proof of this conjecture. We find c = 2.2163823215... - M. F. Hasler, Aug 22 2015

Edited by M. F. Hasler, Aug 14 2015

More terms from M. F. Hasler, Aug 22 2015

A261309 a(n+1) = abs(a(n) - gcd(a(n), 9n+8)), u(1) = 1.

Original entry on oeis.org

1, 0, 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, 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

Offset: 1

M. F. Hasler, Aug 14 2015

nonn

It is conjectured that for all n > 2, u(n) = 0 implies that u(n+1) = 9n+8 is prime, cf. A186261. (This is the sequence {u(n)} mentioned there.)

			a(2) = a(1) - gcd(a(1),9+8) = 1 - 1 = 0.
a(3) = |a(2) - gcd(a(2),9*2+8)| = gcd(0,26) = 26.
a(3+26) = a(29) = 0 and a(29+1) = gcd(0,9*29+8) = 269 is prime.

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

print1(a=1);for(n=1,99,print1(",",a=abs(a-gcd(a,9*n+8))))

cp's OEIS Frontend

A186263 a(n) = 10*b_10(n) + 9, where b_10 lists the indices of zeros of the sequence A261310: u(n) = abs(u(n-1) - gcd(u(n-1), 10n-1)), u(1) = 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

PARI

Formula

Extensions

A261309 a(n+1) = abs(a(n) - gcd(a(n), 9n+8)), u(1) = 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI