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.

A372444 The n-th iterate of 27 with A371094.

Original entry on oeis.org

27, 165, 8021, 12408149, 19607957362005, 32439509492992549521282389, 58947232705679751034215288252890081792789279233365, 259166427025070423330595967015238989905128148712607202753574381749095993394717720069452733214971221
Offset: 0

Views

Author

Antti Karttunen, May 01 2024

Keywords

Crossrefs

Cf. A371094.
Column 7 of A371102, column 14 of A372282.
Column 1 of A372560.
Sequences derived from this one:
A372443 obtained when Reduced Collatz-function R is applied to a(n-1), for n > 0,
A372445 column index of a(n) in array A257852,
A372448 the 2-adic valuation of 1 + 3*a(n), equal to row index of a(n) in array A257852,
A372449 binary lengths minus 1; their first differences: A372451,
A372452 number of terms of A086893 in the interval [a(n), a(1+n)],
A372454 the difference between a(n) and the term of A086893 with the same binary length.

Programs

  • PARI
    A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
    A372444(n) = { my(x=27); while(n, x=A371094(x); n--); (x); };

Formula

a(0) = 27; for n > 0, a(n) = A371094(a(n-1)).

A372449 a(n) = A000523(A372444(n)); One less than the length of binary expansion of the n-th iterate of 27 with A371094.

Original entry on oeis.org

4, 7, 12, 23, 44, 84, 165, 326, 650, 1297, 2590, 5177, 10349, 20695, 41386, 82766, 165527, 331048, 662093, 1324181, 2648358, 5296712, 10593418, 21186832, 42373658, 84747311, 169494616, 338989224, 677978441, 1355956875, 2711913744, 5423827481, 10847654953, 21695309901, 43390619796, 86781239588, 173562479173, 347124958346
Offset: 0

Views

Author

Antti Karttunen, May 04 2024

Keywords

Crossrefs

Programs

Formula

a(n) = A000523(A372444(n)).
a(0) = A372447(0) = 4, and for n > 0, a(n) = A372447(n) + 2*A372448(n-1).

A372362 a(n) is the 2-adic valuation of 1 + 3*{the n-th iterate of 27 with Reduced Collatz-function R}.

Original entry on oeis.org

1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 4, 2, 2, 4, 3, 1, 1, 5, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
Offset: 0

Views

Author

Antti Karttunen, May 06 2024

Keywords

Crossrefs

The first 41 terms form the row 13 of A351122.

Programs

Formula

a(n) = A371093(A372443(n)).

A372454 a(n) = A372444(n) - A086893(1+A372449(n)).

Original entry on oeis.org

6, -48, 2560, -1572864, -3848290697216, 6649092007880460460883968, -18999521285301737936647902825311679255527123058688, 76895533293152762966220781422103876125697362804839499718093497881599910128103059800826635129716736
Offset: 0

Views

Author

Antti Karttunen, May 05 2024

Keywords

Comments

The difference between A372444(n) and the term of A086893 with the same binary length.

Examples

			The term of A086893 that has same binary length as A372444(0) = 27 is 21 [as 21 = 10101_2 in binary, and 27 = 11011_2 in binary], therefore a(0) = 27-21 = 6.
The term of A086893 that has same binary length as A372444(1) = 165 is 213, therefore a(1) = 165-213 = -48.
		

Crossrefs

Programs

Formula

a(n) = A372444(n) - A086893(1+A000523(A372444(n))).
a(0) = A372453(0) = 6; and for n > 0, a(n) = 4^A372448(n-1) * A372453(n).
Showing 1-4 of 4 results.