This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
See A309226.
See A309226.
b(1) = 2 b(2) = 5 b(3) = 0 b(4) = 7 b(5) = 18 b(3) < b(4) < b(5), so 4 is the first term of the sequence.
B := proc(n) option remember ; if n = 1 then 2; else if procname(n-1)-ithprime(n) < 0 then procname(n-1)+ithprime(n) ; else procname(n-1)-ithprime(n) ; fi; fi; end: A135025 := proc(n) option remember ; if n = 1 then 4; else for a from procname(n-1)+1 do if B(a-1) < B(a) and B(a) < B(a+1) then RETURN(a) ; fi; od: fi; end: for n from 1 do printf("%d,\n",A135025(n)) ; od: # R. J. Mathar, Feb 06 2009
B[n_] := B[n] = If[n == 1, 2, If[B[n-1] - Prime[n] < 0, B[n-1] + Prime[n], B[n-1] - Prime[n]]];
a[n_] := a[n] = If[n == 1, 4, For[k = a[n-1]+1, True, k++, If[B[k-1] < B[k] && B[k] < B[k+1], Return[k]]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 16}] (* Jean-François Alcover, Aug 16 2022, after R. J. Mathar *)
Riecaman := proc(a,s,M)
# Start with s, add or subtract a[n], get M terms. If a has w terms, can get M=w+1 terms.
local b,M2,n,t;
if whattype(a) <> list then ERROR("First argument should be a list"); fi;
if a[1]=0 then ERROR("a[1] should not be zero"); fi;
M2 := min(nops(a),M-1);
b:=[s]; t:=s;
for n from 1 to M2 do
if a[n]>t then t:=t+a[n] else t:=t-a[n]; fi; b:=[op(b),t]; od:
b; end;
blocks := proc(a,S) local b,c,d,M,L,n;
# Given a list a, whose leading term has index S, return [b,c,d], where b lists the indices of the low points in a, c lists the values of a at the low points, and d lists the length of runs between the low points.
b:=[]; c:=[]; d:=[]; L:=1;
# if a[1] a low point?
n:=1;
if( (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then
b:=[op(b),n+S-1]; c:=[op(c),a[n]]; d:=[op(d), n-L]; L:=n; fi;
for n from 2 to nops(a)-2 do
# if a[n] a low point?
if( (a[n-1]>a[n]) and (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then
b:=[op(b),n+S-1]; c:=[op(c),a[n]]; d:=[op(d), n-L]; L:=n; fi; od;
[b,c,d]; end;
p0:=[seq(ithprime(n),n=1..100001)]:
q1:=Riecaman(p0,1,100000):
blocks(q1,0); # produces [the present sequence, A324788, A324789]
See Links section.
# Maple program from N. J. A. Sloane, Oct 03 2019; guessb = A325056, guessc = A324791 (this sequence). Digits := 64; f := proc(k,M) local j1, twoL, RL, kprime, Mprime; j1 := 3*k^2+7*k+17/4+2*M; if issqr(j1) then lprint("Beware, perfect square: k,M,j1 are ",k,M,j1); fi; twoL := -k-3/2+evalf(sqrt(j1)) ; RL := floor(twoL/2); Mprime := M+(k+1)^2 - (2*k*RL+3*RL+2*RL^2); kprime := 1+k+2*RL; [twol, RL, Mprime, kprime]; end; guessb:=[0,5]; b:=5; guessc:=[0,5]; c:=5; for i from 1 to 100 do t1:=f(b,c); b:=t1[4]; c:=t1[3]; guessb:=[op(guessb),b]; guessc:=[op(guessc),c]; od: guessb; guessc;
a=b=c=d=n=0; L={0}; While[Length[L] < 22, n++; a=b; b=c; c=d; d=c + If[c < n^2, n^2, -n^2]; If[a > b < c < d, AppendTo[L, b]]]; L (* Giovanni Resta, Oct 01 2019 *)
\\ See Tomas Rokicki's PARI program in A076042.
a=b=c=d=n=0; L={0}; While[Length[L] < 22, n++; a=b; b=c; c=d; d=c + If[c < n^2, n^2, -n^2]; If[a > b < c < d, AppendTo[L, n-2]]]; Differences@ L (* Giovanni Resta, Oct 01 2019 *)
See A324791.
a=b=c=d=n=0; L={0}; While[Length[L] < 22, n++; a=b; b=c; c=d; d=c + If[c < n^2, n^2, -n^2]; If[a > b < c < d, AppendTo[L, n - 2]]]; L (* Giovanni Resta, Oct 01 2019 *)
\\ See PARI program in A076042.
Comments