A106735 Numbers n such that n == prime(m) (mod prime(m+1)) for any m.

2, 3, 5, 7, 8, 11, 12, 13, 14, 17, 18, 19, 20, 23, 24, 26, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 44, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 88, 89, 90, 91, 92, 93, 95

Offset

1,1

Links

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

Example

24 because 24 mod 13 = 11. 40 because 40 mod 7 = 5. 51 because 51 mod 11 = 7.

Maple

N:= 500: # for all terms <= N
p:= 2:
S:= {}:
while p <= N do
  q:= nextprime(p);
  S:= S union {seq(i, i=p..N, q)};
  p:= q;
od:
sort(convert(S, list)); # Robert Israel, Mar 30 2018

Mathematica

nn=150; u={}; Do[lst=Prime[i]+Range[0, Ceiling[nn/Prime[i+1]]]Prime[i+1]; u=Union[u, lst], {i, PrimePi[nn]}]; Intersection[u, Range[nn]] (Noe)

Crossrefs

Sequence in context: A302245 A028728 A286758 * A028743 A082634 A100959

Adjacent sequences: A106732 A106733 A106734 * A106736 A106737 A106738

Keyword

nonn

Author

Christopher M. Tomaszewski (cmt1288(AT)comcast.net), May 14 2005

Extensions

Corrected and extended by T. D. Noe, Oct 25 2005

Status

approved