A127064 -id:A127064 - cp's OEIS frontend

A378417 a(n) is the least k such that A127064(k) = n.

0, 1, 2, 3, 4, 17, 24, 62, 68, 162, 169, 176, 183, 188, 369, 694, 897, 988, 1027, 4183, 5510, 6063, 6341, 6444, 6465, 25787, 32844, 37722, 38811, 39450, 151679, 200946, 226703, 240056, 248947, 430398, 612633, 633473, 635344, 637227, 637237, 637256, 637306, 1095790, 1353912, 1554970, 7045573

Offset: 1

Robert Israel, Nov 25 2024

nonn

a(n) is the least k such that n - 1 iterations of A004648 (k -> prime(k) (mod k)) are needed to reach 0.

			a(6) = 17 because 5 iterations of A004648 starting at 17 result in 0, and every k < 17 requires fewer iterations:
  prime(17) (mod 17) = 59 (mod 17) = 8
  prime(8) (mod 8) = 19 (mod 8) = 3
  prime(3) (mod 3) = 5 (mod 3) = 2
  prime(2) (mod 2) = 3 (mod 2) = 1
  prime(1) (mod 1) = 2 (mod 1) = 0.

Cf. A004648, A127064.

P:= select(isprime, [2,seq(i,i=3..10^8,2)]): nP:= nops(P):
V:= Array(0..nP): count:= 0: R[1]:= 0:
for n from 1 to nP do
V[n]:= V[P[n] mod n]+1;
if V[n] > count then count:= count+1; R[count]:= n fi;
od:
seq(R[i],i=1..count);

A127064(a(n)) = n.

A127066 a(0)=1; for n > 0, a(n) = a(n-1) + a(prime(n)(mod n)), where prime(n) is the n-th prime.

Original entry on oeis.org

1, 2, 4, 8, 16, 18, 20, 28, 36, 54, 108, 162, 164, 168, 170, 174, 192, 228, 256, 364, 526, 634, 802, 972, 1200, 2002, 2974, 3776, 4748, 5550, 6522, 6530, 6538, 6556, 6564, 6618, 6646, 6700, 6862, 7024, 7192, 7366, 7534, 7898, 8126, 8354, 8528, 9500, 16030

Offset: 0

Leroy Quet, Mar 21 2007

nonn

			The 7th prime, 17, is congruent to 3 (mod 7). So a(7) = a(6) + a(3) = 20 + 8 = 28.

Cf. A004648, A127064.

a:=proc(n) if n=0 then 1 else a(n-1)+a(ithprime(n) mod n) fi end: seq(a(n),n=0..55); # Emeric Deutsch, Mar 23 2007

f[l_List] := Block[{n = Length[l]},Append[l, l[[Mod[Prime[n], n] + 1]] + l[[ -1]]]]; Nest[f, {1}, 50] (* Ray Chandler, Mar 23 2007 *)

More terms from Emeric Deutsch and Ray Chandler, Mar 23 2007

cp's OEIS Frontend

A378417 a(n) is the least k such that A127064(k) = n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Formula