cp's OEIS Frontend

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.

Showing 1-4 of 4 results.

A332452 Starting from sigma(n), number of halving steps to reach 1 in '3x+1' problem, or -1 if this never happens.

Original entry on oeis.org

0, 5, 2, 11, 6, 7, 3, 12, 7, 14, 7, 13, 12, 8, 8, 67, 14, 23, 6, 7, 5, 15, 8, 14, 67, 7, 7, 14, 13, 16, 5, 68, 9, 71, 9, 59, 15, 14, 14, 13, 7, 10, 12, 8, 24, 16, 9, 69, 22, 13, 16, 18, 71, 15, 16, 15, 8, 13, 14, 9, 68, 10, 10, 31, 8, 17, 11, 69, 10, 17, 16, 76, 16, 23, 69, 12, 10, 9, 8, 14, 61, 69, 8, 16, 72, 20, 15, 14, 13, 16, 15, 9, 7, 17
Offset: 1

Views

Author

Antti Karttunen, Feb 16 2020

Keywords

Links

Crossrefs

Cf. A000203, A006666, A332209, A332453, A332454.

Programs

Formula

a(n) = A006666(A000203(n)).
a(n) = A332209(n) - A332453(n).

A332455 Starting from sigma(n)+1, number of tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached.

Original entry on oeis.org

0, 0, 1, 0, 5, 2, 6, 0, 5, 6, 2, 5, 5, 7, 7, 0, 6, 1, 1, 9, 8, 6, 7, 5, 0, 9, 40, 10, 39, 42, 8, 0, 7, 41, 7, 4, 11, 5, 10, 33, 9, 43, 4, 1, 11, 42, 7, 39, 5, 38, 42, 7, 41, 34, 42, 34, 6, 33, 5, 16, 39, 43, 12, 0, 1, 42, 3, 15, 43, 42, 42, 7, 3, 10, 39, 3, 43, 16, 6, 14, 5, 15, 1, 17, 41, 8, 34, 4, 33, 46, 2, 16, 44, 42, 34, 39
Offset: 1

Views

Author

Antti Karttunen, Feb 16 2020

Keywords

Links

Crossrefs

Cf. A000203, A006667, A088580, A202274, A332453, A332454.
Cf. also A324294, A332459.

Programs

  • PARI
    A006667(n) = { my(t=0); while(n>1, if(n%2, t++; n=3*n+1, n>>=1)); (t); };
A332455(n) = A006667(1+sigma(n));

Formula

a(n) = A006667(A088580(n)) = A006667(1+sigma(n)).
a(2^n) = 0 for all n >= 0. [Zero occurs at least also at a(25). See A202274]

A332209 Starting from sigma(n), number of halving and tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached.

Original entry on oeis.org

0, 7, 2, 16, 8, 9, 3, 17, 9, 20, 9, 18, 17, 10, 10, 106, 20, 34, 7, 8, 5, 21, 10, 19, 106, 8, 8, 19, 18, 22, 5, 107, 11, 112, 11, 92, 21, 19, 19, 17, 8, 12, 16, 9, 35, 22, 11, 108, 32, 17, 22, 25, 112, 20, 22, 20, 9, 17, 19, 10, 107, 12, 12, 46, 9, 23, 14, 108, 12, 23, 22, 119, 22, 33, 108, 15, 12, 10, 9, 18, 95, 108, 9, 21, 113, 28, 20, 18, 17
Offset: 1

Views

Author

Antti Karttunen, Feb 16 2020

Keywords

Links

Crossrefs

Cf. A000203, A006577, A332452, A332453.

Programs

Formula

a(n) = A006577(A000203(n)).
a(n) = A332452(n) + A332453(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

Views

Author

Antti Karttunen, Feb 16 2020

Keywords

Links

Crossrefs

Cf. A000203, A269174, A332465.
Cf. also A332224, A332209, A332452, A332453.

Programs

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

Formula

a(n) = A269174(A000203(n)) = A269174(sigma(n)).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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