A332465 -id:A332465 - cp's OEIS frontend

A332445 Numbers k of the form 4m+1 for which A087808(sigma(k)) is equal to 2*A087808(k).

2009, 19377, 37809, 59373, 74673, 115677, 270041, 310329, 354609, 357309, 720425, 732321, 841437, 2071737, 2612269, 3131149, 3866461, 3930929, 5172093, 5593981, 7118753, 7903961, 8224173, 9327393, 9438129, 11452321, 12708025, 18857209, 18861889, 18875313, 19110321, 20278269, 20709225, 20950061, 23963597, 24895153

Offset: 1

Antti Karttunen, Feb 14 2020

nonn

Numbers k such that A332224(k) is equal to A087808(2*k) and k == 1 mod 4.
Notably, the only square among the first 299 terms is a(248) = 5808421369 = 76213^2. sigma(5808421369) = 5808497583 == 3 (mod 4) == 7 (mod 8). Of the remaining 298 terms < 2^33, 92 are such that sigma(k) == 6 (mod 8) and 206 are such that sigma(k) == 2 (mod 8), that is, are terms of A332227.
Question: Why the terms come in clusters? Compare also the scatterplots of A087808 and A332224, and a similar sequence A332465.

Intersection of A016813 and A332446.
Cf. also A228058, A332227, A332465.
Cf. A000203, A087808, A286357, A332224, A332225, A332458.

A087808(n) = if(n<1, 0, if(n%2==0, 2*A087808(n/2), A087808((n-1)/2)+1));
isA332445(n) = ((1==(n%4))&&(2*A087808(n)==A087808(sigma(n))));

A332464 Rule 124 one-dimensional cellular automaton applied for one step to the configuration read from the base-2 expansion of sigma(n), then converted back to decimal.

Original entry on oeis.org

3, 7, 12, 11, 14, 28, 24, 19, 31, 54, 28, 44, 22, 56, 56, 35, 54, 107, 60, 126, 96, 108, 56, 76, 35, 126, 120, 88, 38, 216, 96, 67, 112, 126, 112, 255, 110, 76, 88, 254, 126, 224, 124, 252, 214, 216, 112, 140, 91, 239, 216, 230, 126, 152, 216, 152, 240, 254, 76, 504, 70, 224, 248, 131, 252, 432, 204, 134, 224, 432, 216

Offset: 1

Antti Karttunen, Feb 16 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to cellular automata
Index entries for sequences related to sigma(n)

Cf. A000203, A269174, A332465.

Cf. also A332224, A332209, A332452, A332453.

A269174(n) = bitand(bitor(n,n<<1),bitor(bitxor(n,n<<1),bitxor(n,n<<2)));
A332464(n) = A269174(sigma(n));

a(n) = A269174(A000203(n)) = A269174(sigma(n)).

cp's OEIS Frontend

A332445 Numbers k of the form 4m+1 for which A087808(sigma(k)) is equal to 2*A087808(k).

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