A324791 Value of A076042 at its n-th low point.

0, 5, 7, 4, 19, 104, 74, 193, 515, 725, 241, 1948, 2948, 709, 8746, 16451, 48443, 47915, 61369, 41566, 136585, 710582, 476516, 1363747, 3165833, 5491067, 11906702, 15854273, 6895924, 38766838, 63676139, 3935833, 209116033, 219826349, 265573243, 263220940

Offset: 0

Author

N. J. A. Sloane, Sep 04 2019

Keywords

• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..4000 (Terms through a(42) from Giovanni Resta)
• N. J. A. Sloane, Table of n, a(n) for n = 0..10001

Crossrefs

Cf. A076042, A325056, A324792.

If we use primes instead of squares we get A008348, A309226, A324782, A324783.

Programs

Maple

# 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;

Mathematica

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 *)

PARI

\\ See Tomas Rokicki's PARI program in A076042.

Extensions

More terms from Giovanni Resta, Oct 01 2019