A325417 -id:A325417 - cp's OEIS frontend

A325422 Complement of A077477.

3, 4, 5, 7, 13, 17, 19, 21, 23, 25, 28, 29, 31, 33, 34, 37, 41, 43, 45, 46, 49, 53, 55, 61, 65, 67, 71, 73, 77, 79, 81, 82, 85, 89, 91, 95, 97, 101, 103, 105, 106, 109, 113, 115, 117, 118, 119, 121, 125, 127, 129, 133, 137, 139, 141, 142, 145, 149, 151, 153

Offset: 1

Clark Kimberling, Apr 26 2019

These are the numbers 2x + 1 and 3x + 1 as x ranges through the numbers in A077477.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A077477.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{(# - 1)/3, (# - 1)/2}],
IntegerQ]]] &]], {150}]; a;     (* A077477 *)
Complement[Range[Last[a]], a];  (* A325422 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325440 a(n) is the least number not 2a(m)-1 or 3a(m)-1 for any m < n.

Original entry on oeis.org

1, 3, 4, 6, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 32, 33, 34, 36, 37, 40, 42, 45, 46, 48, 49, 50, 51, 52, 54, 56, 57, 58, 60, 61, 64, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 92, 93, 94, 96, 100, 102, 104

Offset: 1

Clark Kimberling, May 02 2019

			The sequence necessarily starts with 1.  The next 2 terms are determined as follows:  because a(1) = 1, the number 2 is disallowed, so that a(2) = 3, whence the numbers 5 and 8 are disallowed, and a(3) = 4.  See A325417 for a guide to related sequences.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A325441.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{(#+1)/2, (#+1)/3}],
IntegerQ]]] &]], {150}]; a          (* A325440 *)
Complement[Range[Last[a]], a]       (* A325441 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325442 a(n) is the least number not 2a(m)-1 or 3a(m) for any m < n.

Original entry on oeis.org

1, 2, 4, 5, 8, 10, 11, 13, 14, 16, 17, 18, 20, 22, 23, 26, 28, 29, 32, 34, 36, 37, 38, 40, 41, 44, 46, 47, 49, 50, 52, 53, 56, 58, 59, 61, 62, 64, 65, 68, 70, 72, 74, 76, 77, 80, 82, 83, 85, 86, 88, 89, 90, 92, 94, 95, 98, 100, 101, 104, 106, 107, 109, 110

Offset: 1

Clark Kimberling, May 02 2019

			The sequence necessarily starts with 1.  The next 2 terms are determined as follows:  because a(1) = 1, the number 3 is disallowed, so that a(2) = 2, whence the numbers 3 and 6 are disallowed, and a(3) = 4.  See A325417 for a guide to related sequences.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A325443.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{(#+1)/2, #/3}],
IntegerQ]]] &]], {150}]; a          (* A325442 *)
Complement[Range[Last[a]], a]       (* A325443 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325462 a(n) is the least number not 2a(m) or 3a(m)-1 for any m < n.

Original entry on oeis.org

1, 3, 4, 5, 7, 9, 12, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 31, 33, 36, 37, 39, 40, 41, 43, 45, 48, 49, 51, 52, 53, 55, 57, 59, 60, 61, 63, 64, 67, 69, 70, 71, 73, 75, 76, 77, 79, 81, 84, 85, 87, 88, 89, 91, 93, 94, 95, 97, 99, 100, 101, 103, 105

Offset: 1

Clark Kimberling, May 01 2019

			The sequence necessarily starts with 1.  The next 2 terms are determined as follows:  because a(1) = 1, the number 2 is disallowed, so that a(2) = 3, whence the numbers 6 and 8 are disallowed, and a(3) = 4.  See A325417 for a guide to related sequences.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A325463.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/2, (#+1)/3}],
IntegerQ]]] &]], {150}]; a          (* A325462 *)
Complement[Range[Last[a]], a]       (* A325463 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325464 a(n) is the least number not 2a(m) or 3a(m)-2 for any m < n.

Original entry on oeis.org

1, 3, 4, 5, 9, 11, 12, 14, 15, 16, 17, 19, 20, 21, 23, 26, 27, 29, 33, 35, 36, 37, 39, 41, 44, 45, 47, 48, 50, 51, 53, 56, 57, 59, 60, 62, 63, 64, 65, 68, 69, 71, 73, 75, 77, 80, 81, 83, 84, 86, 87, 89, 91, 92, 93, 95, 98, 99, 101, 104, 105, 107, 108, 110

Offset: 1

Clark Kimberling, May 01 2019

			The sequence necessarily starts with 1.  The next 2 terms are determined as follows:  because a(1) = 1, the number 2 is disallowed, so that a(2) = 3, whence the numbers 6 and 7 are disallowed, and a(3) = 4.  See A325417 for a guide to related sequences.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A325465.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/2, (#+2)/3}],
IntegerQ]]] &]], {150}]; a          (* A325464 *)
Complement[Range[Last[a]], a]       (* A325465 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325498 Difference sequence of A036668.

Original entry on oeis.org

3, 1, 1, 1, 2, 2, 2, 3, 1, 2, 1, 3, 1, 1, 3, 1, 1, 1, 4, 1, 1, 4, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 1, 2, 2, 4, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 4, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 4, 2, 4, 1, 1, 1, 3, 1, 1, 3, 1

Offset: 1

Clark Kimberling, May 05 2019

See A325417 for a guide to related sequences.

Conjecture: every term is in {1,2,3,4}.

			A036668 is given by A(n) = least number not 2*A(m) or 3*A(m) for any m < n, so that A = (1,4,5,6,7,9,11,...), with differences (3,1,1,1,2,2,...).

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A036668, A325499.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/2}],
IntegerQ]]] &]], {2000}]; a ;       (* A036668 *)
c = Complement[Range[Last[a]], a] ; (* A325424 *)
Differences[a]  (* A325498 *)
Differences[c]  (* A325499 *)
(* Peter J. C. Moses, Apr 23 2019 *)

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = 12/7. - Amiram Eldar, Nov 26 2020

A325445 Difference sequence of A325418.

Original entry on oeis.org

2, 2, 4, 4, 2, 2, 4, 2, 1, 1, 2, 2, 4, 3, 1, 2, 2, 4, 6, 2, 4, 3, 1, 2, 2, 4, 2, 6, 4, 4, 2, 2, 4, 2, 1, 1, 2, 2, 4, 3, 1, 2, 2, 4, 2, 4, 2, 4, 3, 1, 2, 2, 4, 3, 1, 2, 2, 1, 1, 2, 4, 2, 2, 4, 2, 1, 1, 2, 2, 4, 3, 1, 2, 2, 4, 6, 2, 4, 3, 1, 2, 2, 4, 2, 4, 2

Offset: 1

Clark Kimberling, May 03 2019

See A325417 for a guide to related sequences. Conjecture: all the differences are in {1,2,3,4,6}; 5 does not occur; a count of differences d(n) = a(n)-a(n-1) for n=2..10000 follows: 1082 occurrences of d(n) = 1; 2693 of 2; 744 of 3; 1609 of 4, 0 of 5, and 198 of 6.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A325444.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/2, (# - 1)/3}],
IntegerQ]]] &]], {2000}]; a ;       (* A325417 *)
c = Complement[Range[Last[a]], a] ; (* A325418 *)
Differences[a]  (* A325444 *)
Differences[c]  (* A325445 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325494 Difference sequence of A325419.

Original entry on oeis.org

1, 2, 3, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 2, 1, 2, 3, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 2, 3

Offset: 1

Clark Kimberling, May 05 2019

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3}.

			A325419 is given by A(n) = least number not 3*A(m) or 2*A(m)+1 for any m < n, so that A = (1,2,4,7,8,10,11,...), with differences (1,2,3,1,2,1,...).

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A325495.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/3, (# - 1)/2}],
IntegerQ]]] &]], {2000}]; a ;       (* A325419 *)
c = Complement[Range[Last[a]], a] ; (* A325420 *)
Differences[a]  (* A325494 *)
Differences[c]  (* A325495 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325495 Difference sequence of A325420.

Original entry on oeis.org

2, 1, 3, 3, 3, 2, 4, 2, 1, 3, 2, 1, 3, 4, 2, 2, 1, 3, 3, 3, 2, 1, 3, 3, 3, 2, 1, 3, 2, 2, 2, 2, 1, 3, 3, 3, 2, 4, 2, 1, 3, 2, 1, 3, 3, 3, 2, 1, 3, 2, 1, 3, 2, 4, 3, 3, 2, 1, 3, 4, 2, 2, 1, 3, 3, 3, 2, 4, 2, 1, 3, 2, 1, 3, 4, 2, 2, 1, 3, 3, 3, 2, 4, 3, 3, 2

Offset: 1

Clark Kimberling, May 05 2019

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,4}.

Cf. A325417, A325494.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/3, (# - 1)/2}],
IntegerQ]]] &]], {2000}]; a ;       (* A325419 *)
c = Complement[Range[Last[a]], a] ; (* A325420 *)
Differences[a]  (* A325494 *)
Differences[c]  (* A325495 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325496 Difference sequence of A077477.

Original entry on oeis.org

1, 4, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 3, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 4, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 3

Offset: 1

Clark Kimberling, May 05 2019

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,4}.

			A077477 is given by A(n) = least number not 2*A(m)+1 or 3*A(m)+1 for any m < n, so that A = (1,2,6,8,9,10,11,12,14,...), with differences (1,4,2,1,1,1,1,2,...).

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A325417, A077477.

a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{(#-1)/3, (# - 1)/2}],
IntegerQ]]] &]], {2000}]; a ;       (* A077477 *)
c = Complement[Range[Last[a]], a] ; (* A325422 *)
Differences[a]  (* A325496 *)
Differences[c]  (* A325497 *)
(* Peter J. C. Moses, Apr 23 2019 *)

cp's OEIS Frontend

A325422 Complement of A077477.

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A325440 a(n) is the least number not 2*a(m)-1 or 3*a(m)-1 for any m < n.

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A325442 a(n) is the least number not 2*a(m)-1 or 3*a(m) for any m < n.

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A325462 a(n) is the least number not 2*a(m) or 3*a(m)-1 for any m < n.

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A325464 a(n) is the least number not 2*a(m) or 3*a(m)-2 for any m < n.

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A325498 Difference sequence of A036668.

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A325445 Difference sequence of A325418.

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A325494 Difference sequence of A325419.

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A325495 Difference sequence of A325420.

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A325440 a(n) is the least number not 2a(m)-1 or 3a(m)-1 for any m < n.

A325442 a(n) is the least number not 2a(m)-1 or 3a(m) for any m < n.

A325462 a(n) is the least number not 2a(m) or 3a(m)-1 for any m < n.

A325464 a(n) is the least number not 2a(m) or 3a(m)-2 for any m < n.