A287118 Numbers k such that A284644(k) = A284644(k-1) = A284644(k-2) = A284644(k-3).

84, 172, 348, 700, 1404, 2720, 2754, 5448, 10904, 21816, 43640, 87288

Offset: 1

Author

Altug Alkan, following a suggestion from Nathan Fox, May 24 2017

Keywords

• nonn
• more

Comments

For the first twelve terms of this sequence, corresponding values of A284644(k) are 11*2^2, 11*2^3, 11*2^4, 11*2^5, 11*2^6, 11*31*2^2, 3*5*23*2^2, 11*31*2^3, 11*31*2^4, 11*31*2^5, 11*31*2^6, 11*31*2^7 and k - A284644(k) are 40, 84, 172, 348, 700, 1356, 1374, 2720, 5448, 10904, 21816, 43640.

Additionally, a(n) = 2*a(n-1) + 4 for 1 < n < 6 and a(n) = 2*a(n-1) + 8 for 8 < n < 13. In fact, also 5448 = 2720*2 + 8 but there is a(7) = 2754 between 2720 and 5448. In other words, we can partition sequence up to 10^5 as three subsequences: {84, 172, 348, 700, 1404}, {2754}, {2720, 5448, 10904, 21816, 43640, 87288} in order to see curious recursive patterns.

If a(13) exists, it must be greater than 7.5*10^9. - Hans Havermann, May 27 2017

Links

• Altug Alkan, Nathan Fox, and Orhan Ozgur Aybar, On Hofstadter Heart Sequences, Complexity, 2017.

Crossrefs

Cf. A284644.

Programs

Mathematica

a[1]=a[2]=2;a[3]=1;a[n_]:=a[n]=a[n-a[n-1]]+a[n-a[n-2]];SequencePosition[Table[a@n,{n,90000}],{x_,x_,x_,x_}][[;;,2]] (* Harvey P. Dale, Jul 16 2024 *)

PARI

q=vector(10^8); q[1]=q[2]=2;q[3]=1; for(n=4, #q, q[n]=q[n-q[n-1]]+q[n-q[n-2]]); for (k=3, 10^8, if(q[k] == q[k-1] && q[k] == q[k-2] && q[k] == q[k-3], print1(k, ", ")));