login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A204900 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k) is the k-th odd prime. 23
2, 2, 4, 3, 5, 4, 6, 4, 8, 5, 9, 6, 9, 6, 11, 7, 11, 8, 12, 8, 14, 9, 15, 9, 15, 9, 16, 10, 17, 11, 18, 11, 19, 11, 20, 12, 21, 12, 22, 13, 23, 14, 23, 14, 24, 15, 24, 15, 25, 15, 27, 16, 28, 16, 29, 16, 30, 17, 31, 18, 30, 18, 31, 18, 32, 19, 32, 19, 34, 20, 34, 21, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A204892 for a discussion and guide to related sequences

LINKS

Table of n, a(n) for n=1..73.

MATHEMATICA

s[n_] := s[n] = Prime[n + 1]; z1 = 400; z2 = 50;

Table[s[n], {n, 1, 30}]      (* A065091 *)

u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]

Table[u[m], {m, 1, z1}]      (* A204898 *)

v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]

w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]

d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]

Table[d[n], {n, 1, z2}]      (* A204899 *)

k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]

m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]

j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2

Table[k[n], {n, 1, z2}]      (* A204900 *)

Table[j[n], {n, 1, z2}]      (* A204901 *)

Table[s[k[n]], {n, 1, z2}]   (* A204902 *)

Table[s[j[n]], {n, 1, z2}]   (* A204903 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204904 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A000034 conjectured *)

CROSSREFS

Cf. A000040, A065091, A204892.

Sequence in context: A132802 A341947 A268353 * A070803 A071693 A225381

Adjacent sequences:  A204897 A204898 A204899 * A204901 A204902 A204903

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 20 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 25 20:31 EDT 2021. Contains 348256 sequences. (Running on oeis4.)