A275719 -id:A275719 - cp's OEIS frontend

A275717 Numbers n for which A003961(n) > A003961(n-1).

2, 3, 4, 6, 8, 12, 14, 15, 16, 18, 20, 24, 26, 27, 30, 32, 35, 36, 38, 39, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 78, 80, 81, 84, 86, 87, 88, 90, 92, 95, 96, 98, 100, 102, 104, 108, 110, 112, 114, 116, 117, 119, 120, 122, 123, 124, 125, 126, 128, 130, 132, 135, 138, 140, 143, 144

Offset: 1

Antti Karttunen, Aug 07 2016

nonn

One more than the positions of ascents in permutation A048673.

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

One more than A275721.
Cf. A003961, A048673.
Complement: A275718 (apart from 1 which is in neither sequence).
Cf. A029744 (a subsequence, apart from its initial 1).
Cf. also A275719, A275720, A246281, A246282.

f[n_] := Times @@ Map[Prime[PrimePi@ First[#] + 1]^Last[#] &, FactorInteger@ n]; Select[Range@ 145, f[# - 1] < f@ # &] (* Michael De Vlieger, Aug 07 2016 *)

A275718 Numbers n for which A003961(n) < A003961(n-1).

Original entry on oeis.org

5, 7, 9, 10, 11, 13, 17, 19, 21, 22, 23, 25, 28, 29, 31, 33, 34, 37, 41, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 65, 67, 69, 71, 73, 76, 77, 79, 82, 83, 85, 89, 91, 93, 94, 97, 99, 101, 103, 105, 106, 107, 109, 111, 113, 115, 118, 121, 127, 129, 131, 133, 134, 136, 137, 139, 141, 142, 145, 148, 149, 151, 153, 154, 155

Offset: 1

Antti Karttunen, Aug 07 2016

nonn

One more than the positions of descents in permutation A048673.

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

One more than A275722.
Complement: A275717 (apart from 1 which is in neither sequence).
Cf. A003961, A048673.
Cf. also A275719, A275720, A246281, A246282.

f[n_] := Times @@ Map[Prime[PrimePi@ First[#] + 1]^Last[#] &, FactorInteger@ n]; Select[Range@ 155, f[# - 1] > f@ # &] (* Michael De Vlieger, Aug 07 2016 *)

A275721 Numbers n for which A003961(n+1) > A003961(n).

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 14, 15, 17, 19, 23, 25, 26, 29, 31, 34, 35, 37, 38, 39, 41, 43, 44, 47, 49, 51, 53, 55, 59, 61, 62, 63, 65, 67, 69, 71, 73, 74, 77, 79, 80, 83, 85, 86, 87, 89, 91, 94, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 116, 118, 119, 121, 122, 123, 124, 125, 127, 129, 131, 134, 137, 139, 142, 143, 145

Offset: 1

Antti Karttunen, Aug 07 2016

nonn

Positions of the ascents in permutation A048673.

Antti Karttunen, Table of n, a(n) for n = 1..16384

One less than A275717.
Complement: A275722.
Cf. A003961, A048673, A275719.

f[n_] := Times @@ Map[Prime[PrimePi@ First[#] + 1]^Last[#] &, FactorInteger@ n]; Select[Range@ 145, f@ # < f[# + 1] &] (* Michael De Vlieger, Aug 07 2016 *)

A275722 Numbers n for which A003961(n+1) < A003961(n).

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 16, 18, 20, 21, 22, 24, 27, 28, 30, 32, 33, 36, 40, 42, 45, 46, 48, 50, 52, 54, 56, 57, 58, 60, 64, 66, 68, 70, 72, 75, 76, 78, 81, 82, 84, 88, 90, 92, 93, 96, 98, 100, 102, 104, 105, 106, 108, 110, 112, 114, 117, 120, 126, 128, 130, 132, 133, 135, 136, 138, 140, 141, 144, 147, 148, 150, 152, 153, 154

Offset: 1

Antti Karttunen, Aug 07 2016

nonn

Positions of the descents in permutation A048673.

Antti Karttunen, Table of n, a(n) for n = 1..16384

One less than A275718.
Complement: A275721.
Cf. A003961, A048673, A275719.

f[n_] := Times @@ Map[Prime[PrimePi@ First[#] + 1]^Last[#] &, FactorInteger@ n]; Select[Range@ 154, f@ # > f[# + 1] &] (* Michael De Vlieger, Aug 07 2016 *)

A275720 a(1) = 0; for n > 1, if A003961(n) > A003961(n-1) then a(n) = a(n-1) + 1, otherwise if A003961(n) < A003961(n-1), then a(n) = a(n-1) - 1.

Original entry on oeis.org

0, 1, 2, 3, 2, 3, 2, 3, 2, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 2, 3, 2, 3, 4, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 4, 5

Offset: 1

Antti Karttunen, Aug 07 2016

sign

Antti Karttunen, Table of n, a(n) for n = 1..16389

Cf. A003961, A275717, A275718, A275721, A275722.

Cf. also A275719.

a(1) = 0; for n > 1, if A003961(n) > A003961(n-1) then a(n) = a(n-1) + 1, otherwise if A003961(n) < A003961(n-1), then a(n) = a(n-1) - 1.

cp's OEIS Frontend

A275717 Numbers n for which A003961(n) > A003961(n-1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A275718 Numbers n for which A003961(n) < A003961(n-1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A275721 Numbers n for which A003961(n+1) > A003961(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A275722 Numbers n for which A003961(n+1) < A003961(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A275720 a(1) = 0; for n > 1, if A003961(n) > A003961(n-1) then a(n) = a(n-1) + 1, otherwise if A003961(n) < A003961(n-1), then a(n) = a(n-1) - 1.

Views

Author

Keywords

Links

Crossrefs

Formula