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A230399 Smallest k such that when k is divided by all numbers <= k the remainder n occurs most often. 2
1, 7, 26, 23, 34, 53, 118, 167, 188, 69, 178, 179, 372, 349, 374, 375, 376, 377, 498, 499, 356, 501, 502, 503, 1284, 1285, 746, 747, 748, 749, 1038, 1039, 1112, 753, 754, 755, 2136, 2137, 2138, 2139, 2140, 2141, 2562, 2443, 1484, 2445, 1486, 1487, 2568, 2569, 2570, 2571, 2572, 2573, 2934, 2575 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of row in A072528 where it happens first that the n-th column contains the maximum value in the row. - Ralf Stephan, Oct 21 2013

Any nonnegative integer n is the most common remainder during dividing m by all numbers not exceeding m for infinitely many different positive integers m.

LINKS

Table of n, a(n) for n=0..55.

Vladimir Letsko Mathematical Marathon, Problem 181 (in Russian)

EXAMPLE

a(1) = 7 because

1) 7 mod 2 = 7 mod 3 = 7 mod 6 = 1 and the other remainders occur not as often;

2) 7 is the least number such then remainder 1 is more popular than other remainders.

MAPLE

maxrem:=proc(n) local r, n1, i, mx, M, R; n1:=`if`(n mod 2 = 0, n/2-1, (n-1)/2);

R:=Array(0..n1, fill=1):

if n mod 2 = 0 then R[0]:=2 fi:

for i to n1 do r:=n mod i: R[r]:=R[r]+1 od:

mx:=R[0]:M:={0}:

for i to n1 do

if R[i]> mx then mx:=R[i]:M:={i} elif mx=R[i] then M:=M union {i} fi od:

M; end;

Rs:={0}:S:=[[0, 1]]:for n to 6000 do r:=maxrem(n):if nops(r)=1 then r:=op(r):

if not member(r, Rs) then Rs:=Rs union {r}:S:=[op(S), [r, n]] fi fi od:

S:=sort(S);

T:=[]:for i to nops(S) do if S[i, 1]=i-1 then T:=[op(T), S[i, 2]] else break fi od:T;

PROG

(PARI) record(n)=v=vector(n+1); for(d=1, n, t=(n%d)+1; v[t]=v[t]+1); m=0; p=0; for(i=1, n, if(v[i]>m, m=v[i]; p=i)); p

(PARI) for(n=1, 100, for(j=1, 10^6, if(record(j)==n, print1(j, ", "); break)) \\ Ralf Stephan, Oct 21 2013

CROSSREFS

Cf. A230374, A002182, A072528.

Sequence in context: A284786 A262109 A276614 * A246910 A098127 A283427

Adjacent sequences:  A230396 A230397 A230398 * A230400 A230401 A230402

KEYWORD

nonn

AUTHOR

Vladimir Letsko, Oct 18 2013

STATUS

approved

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Last modified February 22 23:44 EST 2020. Contains 332157 sequences. (Running on oeis4.)