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

Author

Neil Fernandez, Sep 01 2008

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Programs

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 *)