A224911 -id:A224911 - cp's OEIS frontend

A238691 a(n) = A190339(n)/A224911(n).

1, 2, 3, 15, 15, 21, 1155, 165, 2145, 51051, 255255, 440895, 440895, 969, 111435, 248834355, 248834355, 2927463, 5898837945, 44352165, 1641030105, 8563193457, 42815967285, 80047243185, 1360803134145, 32898537309, 7731156267615, 1028243783592795, 1028243783592795, 375840831244263

Offset: 0

Paul Curtz, Mar 03 2014

nonn

Are non-repeated terms of A224911(n) (2,3,5,11,17,...) A124588(n+1)?
Are repeated terms of A224911(n) (7,13,19,23,31,37,...) A049591(n+1)? At that sequence, Benoit Cloitre mentions a link to the Bernoulli numbers.
Greatest primes dividing a(n): 1, 2, 3, 5, 5, 7, 11, 11, 13, 17, 17, 19, 19, 19, 23, 29, 29, 29, ... = b(n). It appears that b(n) is A224911(n) with A008578(n), ancient primes, instead of A000040(n).
Hence c(n) = 2, 6, 15, 35, ... = 2, followed by A006094(n+1).

			a(0)=2/2=1, a(1)=6/3=2, a(2)=15/5=3, a(3)=a(4)=105/7=15, ... .

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A060308.

nmax = 40; b[n_] := BernoulliB[n]; b[1] = 1/2; bb = Table[b[n], {n, 0, 2*nmax-1}]; diff = Table[Differences[bb, n], {n, 1, nmax}]; (#/FactorInteger[#][[-1, 1]])& /@ Denominator[Diagonal[diff]]

a(16)-a(25) from Jean-François Alcover, Mar 03 2014

A238737 a(n) = 2*n+2 - A224911(n).

Original entry on oeis.org

0, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 3, 5, 1, 1, 3, 5, 1, 3, 1, 1, 3, 1, 3, 5, 1, 3, 5, 1, 1, 3, 5, 1, 3, 1, 1, 3, 5, 1, 3, 1, 3, 5, 1, 3, 5, 7, 1, 3, 1, 1, 3, 1, 1, 3, 1, 3, 5, 7, 9, 11, 13, 1, 3, 1, 3, 5, 1, 1, 3, 5, 7, 9

Offset: 0

Paul Curtz, Mar 04 2014

nonn

It appears that a(n+2) is successively either one 1 or a string of the odd numbers.
Conjecture: the rank of 1's is A005097(n+1). This is another link between Bernoulli numbers and primes via A190339(n).
Apparently (essentially) a duplicate of A049653. - R. J. Mathar, Mar 30 2014

			a(0)=2-2=0, a(1)=4-3=1, a(2)=6-5=1, a(3)=8-7=1, a(4)=10-7=3.

Cf. A060308, A005408.

A238256 A060308 begins with one 2, one 3, one 5, two 7's, one 11, two 13's, i.e., d(n) = 1, 1, 1, 2, 1, 2, 1, 2, 3, 1,... times the primes (A000040). a(n) uses this distribution with noncomposites (A008578).

Original entry on oeis.org

1, 2, 3, 5, 5, 7, 11, 11, 13, 17, 17, 19, 19, 19, 23, 29, 29, 29, 31, 31, 37, 41, 41, 43, 43, 43, 47, 47, 47, 53, 59, 59, 59, 61, 61, 67, 71, 71, 71, 73, 73, 79, 79, 79, 83, 83, 83, 83, 89, 89, 97, 101, 101, 103, 107, 107, 109, 109, 109, 109, 109, 109, 109

Offset: 1

Paul Curtz, Mar 10 2014

nonn

Paul Curtz, Table of n, a(n) for n = 1..63

Cf. A224911.

lista(nn) = {nn = nn\2; v = vector(nn, i, precprime(2*i)); vnc = concat(1, vector(nn, i, prime(i))); nv = vector(1, i, vnc[i]); ivnc = 1; for (i=2, #v, if (v[i] == v[i-1], nv = concat(nv, nv[#nv]), ivnc++; nv = concat(nv, vnc[ivnc]));); for (i=1, #nv, print1(nv[i], ", "));} \\ Michel Marcus, Mar 20 2014

Conjecture: a(n) is the greatest noncomposite (A008578) dividing A238691(n-1).

cp's OEIS Frontend

A238691 a(n) = A190339(n)/A224911(n).

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A238737 a(n) = 2*n+2 - A224911(n).

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A238256 A060308 begins with one 2, one 3, one 5, two 7's, one 11, two 13's, i.e., d(n) = 1, 1, 1, 2, 1, 2, 1, 2, 3, 1,... times the primes (A000040). a(n) uses this distribution with noncomposites (A008578).

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