A277332 -id:A277332 - cp's OEIS frontend

A085405 Common residues of binomial(3n+2,n+1)/(3n+2) modulo 2.

1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Paul D. Hanna, Jun 29 2003

nonn

The positions of ones are given by A022340 and runs of zeros are given by A085407: both are related to the Fibonacci sequence.

Antti Karttunen, Table of n, a(n) for n = 0..65539
Index entries for characteristic functions

Cf. A005940, A006013, A022340 (ones), A085407 (zeros), A085357, A277332, A323239.

A085405(n) = ((binomial((3*n)+2, n+1)/((3*n)+2))%2); \\ Antti Karttunen, Jan 12 2019

A085405(n) = if(n%2,0,while(n>0, my(nextn=(n>>1)); if(1==(nextn%2)*(n%2), return(0)); n = nextn); (1)); \\ (Much faster than above program) - Antti Karttunen, Jan 12 2019

a(n) = C(3n+2, n+1)/(3n+2) (Mod 2) = A006013(n) (Mod 2), where A006013 is the self-convolution of A001764 (ternary trees).

a(n) = A323239(A005940(1+n)). - Antti Karttunen, Jan 12 2019

A277331 a(n) = A253563(A003714(n)).

Original entry on oeis.org

1, 2, 4, 8, 6, 16, 12, 18, 32, 24, 36, 54, 30, 64, 48, 72, 108, 60, 162, 90, 150, 128, 96, 144, 216, 120, 324, 180, 300, 486, 270, 450, 750, 210, 256, 192, 288, 432, 240, 648, 360, 600, 972, 540, 900, 1500, 420, 1458, 810, 1350, 2250, 630, 3750, 1050, 1470, 512, 384, 576, 864, 480, 1296, 720, 1200, 1944, 1080, 1800, 3000, 840

Offset: 0

Antti Karttunen, Oct 12 2016

nonn

After the initial terms 1, 2 and 4, all other terms can be inductively generated by applying any finite composition-combination of A253560 and A253550 to 4, but with such a restriction that A253550 may not be applied twice in succession.

A permutation of A055932.

Antti Karttunen, Table of n, a(n) for n = 0..10946

Cf. A003714, A055932 (same sequence sorted into ascending order), A253550, A253560, A253563, A122111.

Cf. also A277006, A277332.

(define (A277331 n) (A253563 (A003714 n)))

a(n) = A253563(A003714(n)).

a(n) = A122111(A277006(n)).

A277334 Numbers n, that apart from 2 are all odd and for which n/(largest prime dividing n) is squarefree.

Original entry on oeis.org

1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 111, 113, 115, 119, 121, 123, 127, 129, 131, 133, 137, 139, 141, 143, 145, 147, 149, 151, 155, 157, 159, 161, 163, 165, 167, 169

Offset: 1

Antti Karttunen, Oct 12 2016

nonn

In other words, after 1 and 2, such odd numbers that only the largest prime factor in their prime factorization may have exponent 1 or 2, while all lesser prime factors occur at most once.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Disjoint union of A056911 and A129598(A056911(n)).
Cf. A005117, A008683, A052126.
Cf. A277332 (permutation of this sequence).
Differs from A091377 for the first time at n=36, where a(36)=75, while A091377(36)=77.

with(numtheory): A277334_list := n -> seq(`if`(i=2 or (i::odd and issqrfree(i/ max(factorset(i)))),i,NULL),i=1..n): A277334_list(169); # Peter Luschny, Oct 23 2016

cp's OEIS Frontend

A085405 Common residues of binomial(3n+2,n+1)/(3n+2) modulo 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

PARI

Formula

A277331 a(n) = A253563(A003714(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

Formula

A277334 Numbers n, that apart from 2 are all odd and for which n/(largest prime dividing n) is squarefree.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple