A143801 - OEIS

%I #12 Jul 19 2025 11:57:06

%S 223,359,383,449,503,547,701,797,881,1049,1097,1229,1307,1439,1627,

%T 1733,1759,1987,1997,2027,2221,2287,2309,2437,2477,2579,2617,2647,

%U 2801,2861,2903,2999,3023,3067,3167,3191,3329,3467,3581,3697,3761,3911,3947,4057

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

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

%H Harvey P. Dale, <a href="/A143801/b143801.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

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

%K nonn

%O 1,1

%A _Neil Fernandez_, Sep 01 2008