A204892 -id:A204892 - cp's OEIS frontend

A204893 The index jA204892) for which such j exists, and s(k)=prime(k).

1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 2, 2, 1, 4, 4, 3, 2, 2, 1, 2, 1, 4, 3, 3, 3, 2, 1, 3, 3, 2, 1, 2, 1, 3, 2, 2, 1, 4, 2, 3, 2, 2, 1, 4, 2, 3, 2, 2, 1, 2, 1, 4, 3, 3, 3, 2, 1, 3, 2, 2, 1, 2

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

For a guide to related sequences, see A204892.

Cf. A204892.

Mathematica
```
(See the program at A204892.)
```

A204890 Ordered differences of primes.

Original entry on oeis.org

1, 3, 2, 5, 4, 2, 9, 8, 6, 4, 11, 10, 8, 6, 2, 15, 14, 12, 10, 6, 4, 17, 16, 14, 12, 8, 6, 2, 21, 20, 18, 16, 12, 10, 6, 4, 27, 26, 24, 22, 18, 16, 12, 10, 6, 29, 28, 26, 24, 20, 18, 14, 12, 8, 2, 35, 34, 32, 30, 26, 24, 20, 18, 14, 8, 6, 39, 38, 36, 34, 30, 28, 24, 22

Offset: 1

Clark Kimberling, Jan 20 2012

For a guide to related sequences, see A204892.

A086800, zeros omitted. - R. J. Mathar, Sep 15 2012

			a(1) = prime(2)-prime(1) = 3-2 = 1
a(2) = prime(3)-prime(1) = 5-2 = 3
a(3) = prime(3)-prime(2) = 5-3 = 2
a(4) = prime(4)-prime(1) = 7-2 = 5
a(5) = prime(4)-prime(2) = 7-3 = 4
a(6) = prime(4)-prime(3) = 7-5 = 2
From _Michel Marcus_, May 12 2016: (Start)
As a triangle, first rows are:
  1;
  3, 2;
  5, 4, 2;
  9, 8, 6, 4;
  11, 10, 8, 6, 2; (End)

Cf. A204892, A090321, A086800.

(See the program at A204892.)
With[{prs=Prime[Range[20]]},Flatten[Table[prs[[n]]-Take[prs,n-1], {n,2,Length[prs]}]]] (* Harvey P. Dale, Dec 01 2013 *)

tabl(nn) = {for (n=2, nn, for (m=1, n-1, print1(prime(n) - prime(m), ", ");); print(););} \\ Michel Marcus, May 12 2016

A205558 (A204898)/2 = (prime(k)-prime(j))/2; A086802 without its zeros.

Original entry on oeis.org

1, 2, 1, 4, 3, 2, 5, 4, 3, 1, 7, 6, 5, 3, 2, 8, 7, 6, 4, 3, 1, 10, 9, 8, 6, 5, 3, 2, 13, 12, 11, 9, 8, 6, 5, 3, 14, 13, 12, 10, 9, 7, 6, 4, 1, 17, 16, 15, 13, 12, 10, 9, 7, 4, 3, 19, 18, 17, 15, 14, 12, 11, 9, 6, 5, 2, 20, 19, 18, 16, 15, 13, 12, 10, 7, 6, 3, 1, 22, 21

Offset: 1

Clark Kimberling, Jan 30 2012

nonn

Let p(n) denote the n-th prime.  If c is a positive integer, there are infinitely many pairs (k,j) such that c divides p(k)-p(j).  The set of differences p(k)-p(j) is ordered as a sequence at A204890.  Guide to related sequences:
   c....k..........j..........p(k)-p(j).[p(k)-p(j)]/c
...A133196....A131818....A204898....A205558
...A205560....A205547....A205557....A205675
...A205677....A205678....A205681....A205682
...A205684....A205685....A205688....A205689
...A205691....A205692....A205695....A205696
...A205698....A205699....A205702....A205703
...A205705....A205706....A205709....A205710
...A205712....A205713....A205716....A205717
..A205720....A205721....A205724....A205725
It appears that, as rectangular array, this sequence can be described by A(n,k) is the least m such that there are k primes in the set prime(n) + 2*i for {i=1..n}. - Michel Marcus, Mar 29 2023

			Writing prime(k) as p(k),
p(3)-p(2)=5-3=2
p(4)-p(2)=7-3=4
p(4)-p(3)=7-5=2
p(5)-p(2)=11-3=8
p(5)-p(3)=11-5=6
p(5)-p(4)=11-7=4,
so that the first 6 terms of A205558 are 1,2,1,4,3,2.
The sequence can be regarded as a rectangular array in which row n is given by [prime(n+2+k)-prime(n+1)]/2; a northwest corner follows:
1...2...4...5...7...8....10...13...14...17...19...20
1...3...4...6...7...9....12...13...16...18...19...21
2...3...5...6...8...11...12...15...17...18...20...23
1...3...4...6...9...10...13...15...16...18...21...24
2...3...5...8...9...12...14...15...17...20...23...24
1...3...6...7...10..12...13...15...18...21...22...25
2...5...6...9...11..12...14...17...20...21...24...26
- _Clark Kimberling_, Sep 29 2013

Cf. A205675, A205560, A204892.

s[n_] := s[n] = Prime[n]; z1 = 200; z2 = 80;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]              (* A000040 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]              (* A204890 *)
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] = Delete[w[n], Position[w[n], 0]]
c = 2; t = d[c]                      (* A080036 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}]                  (* A133196 *)
Table[j[n], {n, 1, z2}]                  (* A131818 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204898 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205558 *)

A204922 Ordered differences of Fibonacci numbers.

Original entry on oeis.org

1, 2, 1, 4, 3, 2, 7, 6, 5, 3, 12, 11, 10, 8, 5, 20, 19, 18, 16, 13, 8, 33, 32, 31, 29, 26, 21, 13, 54, 53, 52, 50, 47, 42, 34, 21, 88, 87, 86, 84, 81, 76, 68, 55, 34, 143, 142, 141, 139, 136, 131, 123, 110, 89, 55, 232, 231, 230, 228, 225, 220, 212, 199, 178

Offset: 1

Clark Kimberling, Jan 21 2012

For a guide to related sequences, see A204892. For numbers not in A204922, see A050939.
From Emanuele Munarini, Mar 29 2012: (Start)
Diagonal elements = Fibonacci numbers F(n+1) (A000045)
First column = Fibonacci numbers - 1 (A000071);
Second column = Fibonacci numbers - 2 (A001911);
Row sums = n*F(n+3) - F(n+2) + 2 (A014286);
Central coefficients = F(2*n+1) - F(n+1) (A096140).
(End)

			a(1) = s(2) - s(1) = F(3) - F(2) = 2-1 = 1, where F=A000045;
a(2) = s(3) - s(1) = F(4) - F(2) = 3-1 = 2;
a(3) = s(3) - s(2) = F(4) - F(3) = 3-2 = 1;
a(4) = s(4) - s(1) = F(5) - F(2) = 5-1 = 4.
From _Emanuele Munarini_, Mar 29 2012: (Start)
Triangle begins:
   1;
   2,  1;
   4,  3,  2;
   7,  6,  5,  3;
  12, 11, 10,  8,  5;
  20, 19, 18, 16, 13,  8;
  33, 32, 31, 29, 26, 21, 13;
  54, 53, 52, 50, 47, 42, 34, 21;
  88, 87, 86, 84, 81, 76, 68, 55, 34;
  ... (End)

G. C. Greubel, Rows n=1..100 of triangle, flattened

Cf. A204924, A204892.

/* As triangle */ [[Fibonacci(n+2)-Fibonacci(k+1) : k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Aug 04 2015

Mathematica
```
(See the program at A204924.)
```

create_list(fib(n+3)-fib(k+2),n,0,20,k,0,n); /* Emanuele Munarini, Mar 29 2012 */

{T(n,k) = fibonacci(n+2) - fibonacci(k+1)};
for(n=1,15, for(k=1,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Feb 03 2019

[[fibonacci(n+2) - fibonacci(k+1) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Feb 03 2019

From Emanuele Munarini, Mar 29 2012: (Start)
T(n,k) = Fibonacci(n+2) - Fibonacci(k+1).
T(n,k) = Sum_{i=k..n} Fibonacci(i+1). (End)

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.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

See A204892 for a discussion and guide to related sequences

Cf. A000040, A065091, A204892.

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 *)

A204908 Least k such that n divides s(k)-s(j) for some j in [1,k], where s(k) is the k-th prime >=5.

Original entry on oeis.org

2, 2, 3, 3, 5, 3, 6, 4, 7, 5, 8, 5, 9, 6, 10, 7, 11, 7, 12, 9, 13, 8, 14, 8, 16, 9, 15, 11, 18, 10, 17, 10, 18, 11, 21, 11, 20, 12, 21, 13, 22, 13, 23, 16, 23, 14, 24, 14, 25, 16

Offset: 1

Clark Kimberling, Jan 20 2012

nonn

See A204892 for a discussion and guide to related sequences.

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Cf. A000040, A204892, A204900.

s[n_] := s[n] = Prime[n + 2]; z1 = 400; z2 = 50;
Table[s[n], {n, 1, 30}] (* primes >=5 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]     (* A204906 *)
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}]     (* A204907 *)
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}]     (* A204908 *)
Table[j[n], {n, 1, z2}]     (* A204909 *)
Table[s[k[n]], {n, 1, z2}]  (* A204910 *)
Table[s[j[n]], {n, 1, z2}]  (* A204911 *)

a(n) = {my(p=5, k=1); while(sum(i=5, p-1, isprime(i)&&(p-i)%n==0)==0, p=nextprime(p+1); k++); k; } \\ Jinyuan Wang, Jan 30 2020

A204924 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k)=A000045(k+1) (Fibonacci numbers).

Original entry on oeis.org

2, 3, 4, 4, 5, 5, 5, 6, 7, 6, 6, 6, 7, 9, 12, 7, 9, 7, 7, 7, 8, 10, 12, 12, 9, 8, 9, 10, 8, 17, 8, 8, 8, 9, 21, 12, 14, 10, 18, 17, 11, 9, 10, 10, 12, 12, 9, 12, 13, 9, 17, 9, 9, 9, 10, 17, 12, 12, 25, 22

Offset: 1

Clark Kimberling, Jan 21 2012

nonn

See A204892 for a discussion and guide to related sequences.

			1 divides s(2)-s(1), so a(1)=2
2 divides s(3)-s(1), so a(2)=3
3 divides s(4)-s(2), so a(3)=4
9 divides s(7)-s(3), so a(9)=7

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A000045, A204892.

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 300; z2 = 60;
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]   (* A204922 *)
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}]   (* A204923 *)
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}]       (* A204924 *)
Table[j[n], {n, 1, z2}]       (* A204925 *)
Table[s[k[n]], {n, 1, z2}]    (* A204926 *)
Table[s[j[n]], {n, 1, z2}]    (* A204927 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204928 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204929 *)

A204932 Least k such that n divides k!-j! for some j satisfying 1<=j

Original entry on oeis.org

2, 3, 4, 3, 3, 4, 5, 5, 4, 6, 4, 5, 9, 6, 6, 5, 5, 4, 5, 6, 6, 4, 4, 5, 6, 9, 7, 8, 6, 6, 10, 5, 7, 6, 8, 7, 13, 5, 9, 6, 7, 6, 11, 7, 7, 8, 10, 5, 8, 6, 6, 9, 12, 7, 8, 8, 5, 6, 5, 6, 16, 10, 8, 9, 14, 7, 8, 11, 8, 8, 9, 7, 8, 13, 6, 7, 12, 9, 14, 7, 10, 7, 19, 8, 11, 11, 6, 7, 10, 7

Offset: 1

Clark Kimberling, Jan 21 2012

nonn

See A204892 for a discussion and guide to related sequences.

			1 divides 2!-1!, so a(1)=2
2 divides 3!-2!, so a(2)=3
3 divides 4!-3!, so a(3)=4
13 divides 9!-4!, so a(13)=9

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000142, A204892.

f:= proc(n) local t, k, V;
  t:= 1:
  for k from 1 do
    t:= t*k mod n;
    if assigned(V[t]) then return k else V[t]:= k fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 11 2024

s[n_] := s[n] = n!; z1 = 80; z2 = 60;
Table[s[n], {n, 1, 30}]     (* A000142 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]     (* A204930 *)
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}]     (* A204931 *)
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}]        (* A204932 *)
Table[j[n], {n, 1, z2}]        (* A204933 *)
Table[s[k[n]], {n, 1, z2}]     (* A204934 *)
Table[s[j[n]], {n, 1, z2}]     (* A204935 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204936 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204937 *)

A204982 Least k such that n divides k!! - j!! for some j satisfying 1 <= j < k.

Original entry on oeis.org

2, 3, 4, 5, 4, 4, 4, 6, 6, 6, 6, 5, 5, 5, 6, 8, 7, 7, 7, 6, 8, 12, 6, 8, 10, 7, 10, 8, 14, 7, 8, 10, 6, 7, 9, 10, 12, 10, 9, 6, 8, 8, 15, 12, 6, 6, 6, 8, 11, 11, 7, 7, 17, 10, 12, 8, 7, 16, 9, 9

Offset: 1

Clark Kimberling, Jan 22 2012

nonn

See A204892 for a discussion and guide to related sequences.

			Example 1. Using 1!! = 1, 2!! = 2, 3!! = 3, 4!! = 8, we verify that a(5) = 5 as follows: The values of 4!!-j!! for j = 1,2,3 are 7,6,5, respectively, so 5 divides 4!! - 3!!, and so for k = 4 there is a number j as required.  On the other hand, it is easy to check that for k = 1,2,3, there is no such j.
Example 2. To see that a(6) = 4, we already noted that 6 divides 4!!-2!! in Example 1, and it is easy to check that for k = 1,2,3, the number 6 does not divide k!! - j!! for any j satisfying 1 <=j < k.

Cf. A006882, A204892, A205104.

s[n_] := s[n] = n!!; z1 = 400; z2 = 60;
Table[s[n], {n, 1, 30}]  (* A006882 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]  (* A204912 *)
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}]     (* A204913 *)
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}]     (* A204982 *)
Table[j[n], {n, 1, z2}]     (* A205100 *)
Table[s[k[n]], {n, 1, z2}]  (* A205101 *)
Table[s[j[n]], {n, 1, z2}]  (* A205102 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A205103 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205104 *)

Edited by Clark Kimberling, Apr 15 2020

A204987 Least k such that n divides 2^k - 2^j for some j satisfying 1 <= j < k.

Original entry on oeis.org

2, 2, 3, 3, 5, 3, 4, 4, 7, 5, 11, 4, 13, 4, 5, 5, 9, 7, 19, 6, 7, 11, 12, 5, 21, 13, 19, 5, 29, 5, 6, 6, 11, 9, 13, 8, 37, 19, 13, 7, 21, 7, 15, 12, 13, 12, 24, 6, 22, 21, 9, 14, 53, 19, 21, 6, 19, 29, 59, 6, 61, 6, 7, 7, 13, 11, 67, 10, 23, 13, 36, 9, 10, 37, 21, 20, 31, 13, 40, 8, 55, 21, 83, 8, 9, 15, 29, 13

Offset: 1

Clark Kimberling, Jan 21 2012

nonn

See A204892 for a discussion and guide to related sequences.

			1 divides 2^2 - 2^1, so a(1)=2;
2 divides 2^2 - 2^1, so a(2)=2;
3 divides 2^3 - 2^1, so a(3)=3;
4 divides 2^3 - 2^2, so a(4)=3;
5 divides 2^5 - 2^1, so a(5)=5.

Antti Karttunen, Table of n, a(n) for n = 1..6556

Cf. A000079, A007733, A007814, A054703, A204892, A204988.

s[n_] := s[n] = 2^n; z1 = 1000; z2 = 50;
Table[s[n], {n, 1, 30}]     (* A000079 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]     (* A204985 *)
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}]     (* A204986 *)
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}]     (* A204987 *)
Table[j[n], {n, 1, z2}]     (* A204988 *)
Table[s[k[n]], {n, 1, z2}]  (* A204989 *)
Table[s[j[n]], {n, 1, z2}]  (* A140670 ? *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204991 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204992 *)
%%/2  (* A204990=(1/2)*A204991 *)

A204987etA204988(n) = { my(k=2); while(1,for(j=1,k-1,if(!(((2^k)-(2^j))%n),return([k,j]))); k++); }; \\ (Computes also A204988 at the same time) - Antti Karttunen, Nov 19 2017

a(n)={my(k=valuation(n,2)); max(k, 1) + znorder(Mod(2, n>>k))} \\ Andrew Howroyd, Aug 08 2018

a(n) = max(1, A007814(n)) + A007733(n). - Andrew Howroyd, Aug 08 2018

More terms from Antti Karttunen, Nov 19 2017

cp's OEIS Frontend

A204893 The index jA204892) for which such j exists, and s(k)=prime(k).

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A204890 Ordered differences of primes.

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A205558 (A204898)/2 = (prime(k)-prime(j))/2; A086802 without its zeros.

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A204922 Ordered differences of Fibonacci numbers.

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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.

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A204908 Least k such that n divides s(k)-s(j) for some j in [1,k], where s(k) is the k-th prime >=5.

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A204924 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k)=A000045(k+1) (Fibonacci numbers).

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A204932 Least k such that n divides k!-j! for some j satisfying 1<=j

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