A143801 Primes with sum of remainders modulo all smaller primes which is smaller than this sum for the preceding prime.

223, 359, 383, 449, 503, 547, 701, 797, 881, 1049, 1097, 1229, 1307, 1439, 1627, 1733, 1759, 1987, 1997, 2027, 2221, 2287, 2309, 2437, 2477, 2579, 2617, 2647, 2801, 2861, 2903, 2999, 3023, 3067, 3167, 3191, 3329, 3467, 3581, 3697, 3761, 3911, 3947, 4057

Offset

1,1

Comments

These are the k-th primes, where A033955(k) < A033955(k-1)

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

When divided by 2,3,5,7,11,...., the number 211 gives remainders 1,1,1,1,2, etc., which sum to 1615 and the number 223 gives remainders 1,1,3,6,3, etc., which sum to 1573. 1573 is smaller than 1615, so 223 is in the sequence.

Mathematica

Prime[#]&/@(Flatten[Position[Differences[Table[Total[Mod[p, Prime[Range[PrimePi[p]]]]], {p, Prime[Range[600]]}]], _?(#<0&)]]+1) (* Harvey P. Dale, Jul 18 2025 *)

Crossrefs

Sequence in context: A152824 A142386 A102950 * A118818 A142437 A142773

Adjacent sequences: A143798 A143799 A143800 * A143802 A143803 A143804

Keyword

nonn

Author

Neil Fernandez, Sep 01 2008

Status

approved