A249746 -id:A249746 - cp's OEIS frontend

A249735 Odd bisection of A003961: Replace in 2n-1 each prime factor p(k) with prime p(k+1).

1, 5, 7, 11, 25, 13, 17, 35, 19, 23, 55, 29, 49, 125, 31, 37, 65, 77, 41, 85, 43, 47, 175, 53, 121, 95, 59, 91, 115, 61, 67, 275, 119, 71, 145, 73, 79, 245, 143, 83, 625, 89, 133, 155, 97, 187, 185, 161, 101, 325, 103, 107, 385, 109, 113, 205, 127, 203, 425, 209, 169, 215, 343, 131, 235, 137, 253, 875, 139, 149, 265, 221, 217, 605, 151

Offset: 1

Antti Karttunen, Nov 23 2014

nonn

This has the same terms as A007310 (Numbers congruent to 1 or 5 mod 6), but in different order. Apart from 1, they are the numbers that occur below the first two rows of arrays like A246278 and A083221 (A083140).

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

Cf. A249734 (the other bisection of A003961).

Cf. also A007310 (A038179), A249746.

(define (A249735 n) (A003961 (+ n n -1)))

a(n) = A003961(2n - 1).
a(n) = A007310(A249746(n)). [Permutation of A007310, Numbers congruent to 1 or 5 mod 6.]
Other identities. For all n >= 1:
A007310(n) = a(A249745(n)).
A246277(5*a(A048673(n))) = n.
A246277(5*a(n)) = A064216(n).

A249826 Permutation of natural numbers: a(n) = A078898(A003961(A003961(A003961(2*n)))).

Original entry on oeis.org

1, 2, 3, 14, 4, 21, 5, 92, 33, 25, 6, 144, 7, 32, 39, 641, 8, 226, 9, 170, 50, 36, 10, 1007, 46, 43, 355, 223, 11, 267, 12, 4482, 56, 55, 59, 1582, 13, 58, 68, 1190, 15, 350, 16, 249, 420, 70, 17, 7043, 78, 316, 86, 301, 18, 2485, 66, 1555, 91, 77, 19, 1869, 20, 81, 549, 31374, 80, 391, 22, 379, 109, 413, 23, 11068, 24, 88, 496, 406, 87, 473, 26, 8324, 3905, 99, 27

Offset: 1

Antti Karttunen, Dec 06 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..127
Index entries for sequences that are permutations of the natural numbers

Inverse: A249825.
Row 4 of A249822.
Cf. A003961, A251722, A048673, A078898, A246278, A249824, A249746, A250476.

(define (A249826 n) (A078898 (A003961 (A003961 (A003961 (* 2 n))))))

a(n) = A078898(A003961(A003961(A003961(2*n)))).
a(n) = A078898(A246278(4,n)).
As a composition of other permutations:
a(n) = A250476(A249824(n)).
a(n) = A250476(A249746(A048673(n))). [Composition of the first three rows of array A251722.]

A353420 a(n) = A126760(A003961(n)).

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 1, 9, 3, 5, 2, 6, 4, 12, 1, 7, 9, 8, 3, 19, 5, 10, 2, 17, 6, 42, 4, 11, 12, 13, 1, 22, 7, 26, 9, 14, 8, 29, 3, 15, 19, 16, 5, 59, 10, 18, 2, 41, 17, 32, 6, 20, 42, 31, 4, 39, 11, 21, 12, 23, 13, 92, 1, 40, 22, 24, 7, 49, 26, 25, 9, 27, 14, 82, 8, 48, 29, 28, 3, 209, 15, 30, 19, 45, 16, 52, 5, 33

Offset: 1

Antti Karttunen, Apr 20 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from indices in prime factorization

Cf. A000265, A003602, A003961, A048673, A126760, A249735, A249745, A249746.

Cf. A353335 (Dirichlet inverse), A353336 (sum with it).

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
A353420(n) = A126760(A003961(n));

a(n) = A126760(A003961(n)) = A249746(A003602(n)) = A126760(A249735(A003602(n))).
a(n) = A353336(4*n) = A353336(n) - A353335(n).
For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
For all n >= 1, A249745(a(n)) = A003602(n).

cp's OEIS Frontend

A249735 Odd bisection of A003961: Replace in 2n-1 each prime factor p(k) with prime p(k+1).

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A249826 Permutation of natural numbers: a(n) = A078898(A003961(A003961(A003961(2*n)))).

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A353420 a(n) = A126760(A003961(n)).

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