A332454 -id:A332454 - cp's OEIS frontend

A332459 Odd part of 1+sigma(n).

1, 1, 5, 1, 7, 13, 9, 1, 7, 19, 13, 29, 15, 25, 25, 1, 19, 5, 21, 43, 33, 37, 25, 61, 1, 43, 41, 57, 31, 73, 33, 1, 49, 55, 49, 23, 39, 61, 57, 91, 43, 97, 45, 85, 79, 73, 49, 125, 29, 47, 73, 99, 55, 121, 73, 121, 81, 91, 61, 169, 63, 97, 105, 1, 85, 145, 69, 127, 97, 145, 73, 49, 75, 115, 125, 141, 97, 169, 81, 187, 61, 127

Offset: 1

Antti Karttunen, Feb 16 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to binary expansion of n
Index entries for sequences related to sigma(n)

Cf. A000203, A000265, A002487, A088580, A161942, A202274, A324294, A332454, A332455.

A332459(n) = { my(s=1+sigma(n)); (s>>valuation(s,2)); };

a(n) = A000265(A088580(n)) = A000265(1+sigma(n)).
A002487(a(n)) = A324294(n).
a(2^n) = 0 for all n >= 0. [Zero occurs at least also at a(25). See A202274]

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

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 3x+1 (or Collatz) problem
Index entries for sequences related to sigma(n)

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

A006666(n) = { my(t); while(n>1, if(n%2, n=3*n+1, n>>=1; t++)); (t); }; \\ From A006666
A332452(n) = A006666(sigma(n));

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

Antti Karttunen, Feb 16 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for sequences related to sigma(n)

Cf. A000203, A006667, A088580, A202274, A332453, A332454.

Cf. also A324294, A332459.

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));

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]

cp's OEIS Frontend

A332459 Odd part of 1+sigma(n).

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula