A299988 -id:A299988 - cp's OEIS frontend

A299982 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 2, and no term occurs twice.

0, 2, 10, 11, 1, 19, 3, 9, 12, 8, 4, 16, 5, 7, 13, 14, 6, 15, 17, 25, 27, 35, 37, 45, 47, 55, 57, 63, 29, 23, 39, 33, 49, 43, 59, 53, 67, 54, 18, 24, 28, 34, 38, 44, 48, 64, 56, 26, 36, 46, 66, 58, 62, 20, 22, 30, 32, 40, 42, 50, 52, 60, 61, 21, 31, 41, 51, 69, 73, 79, 83, 89, 93, 99, 101, 71, 81, 91, 109, 92, 70

Offset: 0

M. F. Hasler and Eric Angelini, Feb 22 2018

A permutation of the nonnegative integers.

Cf. A299972 (analog with positive terms), A299957 (analog with digit 1), A299970, A299983, ..., A299988, A299969 (digit 0, 3, ..., 9).

a(n,f=1,d=2,a=0,u=[a])={for(n=1,n,f&&if(f==1,print1(a","),write(f,n-1," "a));for(k=u[1]+1,oo,setsearch(u,k)&&next;setsearch(Set(digits(a+k)),d)&&(a=k)&&break);u=setunion(u,[a]);u[2]==u[1]+1&&u=u[^1]);a}

A299980 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 0, and no term occurs twice.

Original entry on oeis.org

1, 10, 2, 5, 4, 15, 6, 17, 12, 9, 20, 3, 30, 7, 29, 14, 22, 23, 35, 8, 13, 16, 19, 11, 28, 18, 25, 24, 21, 40, 26, 27, 38, 37, 46, 44, 32, 33, 31, 34, 45, 36, 39, 50, 41, 49, 42, 43, 47, 60, 48, 55, 51, 53, 57, 54, 52, 58, 65, 56, 59, 68, 70, 61, 64, 63, 62, 66, 75, 67, 76, 79, 71, 80, 69, 73, 74, 82, 72, 84, 81, 87, 90, 77, 78, 85, 83, 88, 91

Offset: 1

M. F. Hasler, Feb 22 2018

A permutation of the positive integers.

			a(1) = 1 is the least positive integer, and a(1) has no other constraint to satisfy.
a(2) = 10 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 10 has a digit 0.
a(3) = 2 is the smallest available positive integer, and such that a(3)*a(2) (= 20) has a digit 0.
a(4) = 5 is the least positive integer not in {1, 2, 10} such that a(4)*a(3) (= 10) has a digit 0: The smaller choices 2, 3 and 4 do not satisfy this.

Cf. A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979: analog with digit 1, ..., 9.

Cf. A299957, A299969, ..., A299988: analog with addition instead of multiplication, and different digits.

A299980(n,f=1,d=0,a=1,u=[a])={for(n=2,n,f&&if(f==1,print1(a","),write(f,n-1," "a)); for(k=u[1]+1,oo, setsearch(u,k)&&next;setsearch(Set(digits(a*k)),d)&&(a=k)&&break);u=setunion(u,[a]);while(#u>1&&u[2]==u[1]+1,u=u[^1]));a}

A299981 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 1, and no term occurs twice.

Original entry on oeis.org

1, 10, 11, 12, 9, 2, 5, 3, 4, 25, 6, 17, 7, 13, 8, 14, 15, 21, 31, 23, 18, 34, 24, 38, 27, 19, 22, 28, 29, 35, 26, 16, 32, 33, 36, 30, 37, 39, 40, 41, 42, 43, 44, 45, 47, 46, 59, 20, 50, 62, 51, 61, 52, 56, 57, 53, 55, 58, 54, 65, 48, 66, 63, 67, 73, 70, 74, 69, 49, 64, 80, 77, 82, 75, 68, 76, 81, 71, 72, 78, 79, 85, 60, 86, 83, 87, 91, 90, 89

Offset: 1

M. F. Hasler, Feb 22 2018

A permutation of the positive integers.

			a(1) = 1 is the least positive integer, and a(1) has no other constraint to satisfy.
a(2) = 10 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 10 has a digit 1. (For all small choices 2, ..., 9 this is not the case.)
a(3) = 11 is the smallest positive integer not in {1, 10} such that a(3)*a(2) (= 110) has a digit 1.
a(4) = 12 is the least positive integer not in {1, 10, 11} such that a(4)*a(3) (= 132) has a digit 1: All smaller choices 2, 3, ..., 9 do not satisfy this.

Cf. A299980, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979: analog with digit 0, 2, ..., 9.

Cf. A299957, A299969, ..., A299988: analog with addition instead of multiplication, and different digits.

A299981(n,f=1,d=1,a=1,u=[a])={for(n=2,n,f&&if(f==1,print1(a","),write(f,n-1," "a)); for(k=u[1]+1,oo, setsearch(u,k)&&next;setsearch(Set(digits(a*k)),d)&&(a=k)&&break);u=setunion(u,[a]);while(#u>1&&u[2]==u[1]+1,u=u[^1]));a}

A299952 The sum a(n) + a(n+1) is a substring of the concatenation of all terms up to a(n+1). Lexicographic first sequence of positive integers without duplicate terms having this property.

Original entry on oeis.org

1, 10, 99, 11, 80, 19, 61, 30, 31, 49, 12, 2, 4, 5, 3, 6, 7, 15, 9, 13, 17, 14, 8, 16, 20, 25, 23, 22, 26, 27, 18, 34, 28, 21, 24, 29, 32, 35, 36, 44, 37, 43, 38, 33, 41, 39, 42, 40, 51, 45, 46, 47, 52, 57, 53, 56, 54, 55, 63, 59, 50, 60, 58, 64, 66, 65, 74, 48, 62, 68, 71, 77, 72, 67, 78, 70

Offset: 1

Eric Angelini and Lars Blomberg, Feb 22 2018

The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that does not lead to a contradiction.

This is probably a permutation of the natural numbers (after 10000 terms, the smallest integer not yet present is 9990).

			a(1) + a(2) = 1 + 10 = 11 and “11” is visible in [1,10]
a(2) + a(3) = 10 + 99 = 109 and “109” is visible in [10,99]
a(3) + a(4) = 99 + 11 = 110 and “110” is visible in [1,10]
a(4) + a(5) = 11 + 80 = 91 and “91” is visible in [99,11]
a(5) + a(6) = 80 + 19 = 99 and “99” is visible in [99]
a(6) + a(7) = 19 + 61 = 80 and “80” is visible in [80]
...

Lars Blomberg, Table of n, a(n) for n = 1..10000

Cf. A300000.
For a different constraint on a(n)+a(n+1) (must have a digit '1'), see A299957 and A299970, A299982, ..., A299988, A299969  (nonnegative analog with digit 0, 2, ..., 9), A299971, A299972, ..., A299979 (positive analog with digit 0, 2, ..., 9).
Cf. A299980, A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979 for the analog using multiplication: a(n)*a(n+1) has a digit 0, resp. 1, ..., resp. 9.

Nest[Function[a, Append[a, Block[{k = 1, d}, While[Nand[FreeQ[a, k], SequenceCount[Flatten@ IntegerDigits[Append[a, k]], IntegerDigits[a[[-1]] + k]] > 0], k++]; k]]], {1}, 75] (* Michael De Vlieger, Feb 22 2018 *)

a(n,show=1,a=1,s=a,u=[a],t,m)={for(n=2,n, show&&print1(a","); for(k=u[1]+1,oo, setsearch(u,k)&&next;m=Mod(a+k,10^#Str(a+k));t=s*10^#Str(k)+k; until(k>=t\=10,t==m&&(a=k)&&break(2)));s=s*10^#Str(a)+a;u=setunion(u,[a]); u[2]==u[1]+1&&u=u[^1]);a} \\ M. F. Hasler, Feb 22 2018

A299978 Lexicographic first sequence of positive integers such that a(n) + a(n+1) has a digit 8, and no term occurs twice.

Original entry on oeis.org

1, 7, 11, 17, 21, 27, 31, 37, 41, 39, 9, 19, 29, 49, 32, 6, 2, 16, 12, 26, 22, 36, 42, 38, 10, 8, 20, 18, 30, 28, 40, 43, 5, 3, 15, 13, 25, 23, 35, 33, 45, 44, 4, 14, 24, 34, 46, 52, 56, 62, 66, 72, 76, 82, 86, 92, 88, 50, 48, 60, 58, 70, 68, 80, 78, 90, 91, 47, 51, 57, 61, 67, 71, 77, 81, 87, 93, 55, 53, 65, 63, 75, 73, 85, 83, 95, 89, 59, 69, 79, 99

Offset: 1

M. F. Hasler and Eric Angelini, Feb 22 2018

A permutation of the positive integers.

Cf. A299988 (analog with nonnegative terms), A299957 (analog with digit 1), A299971, A299972, ..., A299979 (digit 0, 2, ..., 9).

a(n,f=1,d=8,a=1,u=[a])={for(n=2,n,f&&if(f==1,print1(a","),write(f,n-1," "a));for(k=u[1]+1,oo,setsearch(u,k)&&next;setsearch(Set(digits(a+k)),d)&&(a=k)&&break);u=setunion(u,[a]);u[2]==u[1]+1&&u=u[^1]);a}

A299983 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 3, and no term occurs twice.

Original entry on oeis.org

0, 3, 10, 13, 17, 6, 7, 16, 14, 9, 4, 19, 11, 2, 1, 12, 18, 5, 8, 15, 20, 23, 30, 33, 40, 43, 50, 53, 60, 63, 67, 26, 27, 36, 37, 46, 47, 56, 57, 66, 64, 29, 24, 39, 34, 49, 44, 59, 54, 69, 61, 22, 21, 32, 31, 42, 41, 52, 51, 62, 68, 25, 28, 35, 38, 45, 48, 55, 58, 65, 70, 73, 80, 83, 90, 93, 100, 103, 110, 113, 117, 76, 77, 86, 87, 96, 97, 106, 107

Offset: 0

M. F. Hasler and Eric Angelini, Feb 22 2018

A permutation of the nonnegative integers.

Cf. A299973 (analog with positive terms), A299957 (analog with digit 1), A299970, A299982, ..., A299988, A299969 (digit 0, 2, ..., 9).

a(n,f=1,d=3,a=0,u=[a])={for(n=1,n,f&&if(f==1,print1(a","),write(f,n-1," "a));for(k=u[1]+1,oo,setsearch(u,k)&&next;setsearch(Set(digits(a+k)),d)&&(a=k)&&break);u=setunion(u,[a]);u[2]==u[1]+1&&u=u[^1]);a}

A299987 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 7, and no term occurs twice.

Original entry on oeis.org

0, 7, 10, 17, 20, 27, 30, 37, 33, 4, 3, 14, 13, 24, 23, 34, 36, 1, 6, 11, 16, 21, 26, 31, 39, 8, 9, 18, 19, 28, 29, 38, 32, 5, 2, 15, 12, 25, 22, 35, 40, 47, 50, 57, 60, 67, 70, 77, 80, 87, 83, 44, 43, 54, 53, 64, 63, 74, 73, 84, 86, 41, 46, 51, 56, 61, 66, 71, 76, 81, 89, 48, 49, 58, 59, 68, 69, 78, 79, 88, 82, 45, 42, 55, 52, 65, 62, 75, 72, 85, 90

Offset: 0

M. F. Hasler and Eric Angelini, Feb 22 2018

A permutation of the nonnegative integers.

Cf. A299977 (analog with positive terms), A299957 (analog with digit 1), A299970, A299982..A299988, A299969 (digit 0, 2..8, 9).

a(n,f=1,d=7,a=0,u=[a])={for(n=1,n,f&&if(f==1,print1(a","),write(f,n-1," "a));for(k=u[1]+1,oo,setsearch(u,k)&&next;setsearch(Set(digits(a+k)),d)&&(a=k)&&break);u=setunion(u,[a]);u[2]==u[1]+1&&u=u[^1]);a}

A299984 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 4, and no term occurs twice.

Original entry on oeis.org

0, 4, 10, 14, 20, 21, 3, 1, 13, 11, 23, 17, 7, 27, 15, 9, 5, 19, 22, 2, 12, 28, 6, 8, 16, 18, 24, 25, 29, 35, 39, 45, 49, 55, 59, 65, 69, 71, 33, 31, 43, 41, 53, 51, 63, 61, 73, 67, 37, 47, 57, 77, 64, 30, 34, 40, 44, 50, 54, 60, 74, 66, 38, 26, 48, 36, 58, 46, 68, 56, 78, 62, 32, 42, 52, 72, 70, 75, 79, 85, 89, 95, 99, 105, 109, 115, 119, 121, 83

Offset: 0

M. F. Hasler and Eric Angelini, Feb 22 2018

A permutation of the nonnegative integers.

Cf. A299974 (analog with positive terms), A299957 (analog with digit 1), A299970, A299982, ..., A299988, A299969 (digit 0, 2, ..., 8, 9).

a(n,f=1,d=4,a=0,u=[a])={for(n=1,n,f&&if(f==1,print1(a","),write(f,n-1," "a));for(k=u[1]+1,oo,setsearch(u,k)&&next;setsearch(Set(digits(a+k)),d)&&(a=k)&&break);u=setunion(u,[a]);u[2]==u[1]+1&&u=u[^1]);a}

A299985 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 5, and no term occurs twice.

Original entry on oeis.org

0, 5, 10, 15, 20, 25, 26, 9, 6, 19, 16, 29, 21, 4, 1, 14, 11, 24, 27, 8, 7, 18, 17, 28, 22, 3, 2, 13, 12, 23, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 76, 39, 36, 49, 46, 59, 56, 69, 66, 79, 71, 34, 31, 44, 41, 54, 51, 64, 61, 74, 77, 38, 37, 48, 47, 58, 57, 68, 67, 78, 72, 33, 32, 43, 42, 53, 52, 63, 62, 73, 80, 85, 90, 95, 100, 105, 110, 115, 120

Offset: 0

M. F. Hasler and Eric Angelini, Feb 22 2018

A permutation of the nonnegative integers.

Cf. A299975 (analog with positive terms), A299957 (analog with digit 1), A299970, A299982..A299988, A299969 (digit 0, 2..8, 9).

a(n,f=1,d=5,a=0,u=[a])={for(n=1,n,f&&if(f==1,print1(a","),write(f,n-1," "a));for(k=u[1]+1,oo,setsearch(u,k)&&next;setsearch(Set(digits(a+k)),d)&&(a=k)&&break);u=setunion(u,[a]);u[2]==u[1]+1&&u=u[^1]);a}

A299986 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 6, and no term occurs twice.

Original entry on oeis.org

0, 6, 10, 16, 20, 26, 30, 31, 5, 1, 15, 11, 25, 21, 35, 27, 9, 7, 19, 17, 29, 32, 4, 2, 14, 12, 24, 22, 34, 28, 8, 18, 38, 23, 3, 13, 33, 36, 40, 46, 50, 56, 60, 66, 70, 76, 80, 81, 45, 41, 55, 51, 65, 61, 75, 71, 85, 77, 39, 37, 49, 47, 59, 57, 69, 67, 79, 82, 44, 42, 54, 52, 64, 62, 74, 72, 84, 78, 48, 58, 68, 88, 73, 43, 53, 63, 83, 86, 90, 96, 100

Offset: 0

M. F. Hasler and Eric Angelini, Feb 22 2018

A permutation of the nonnegative integers.

Cf. A299976 (analog with positive terms), A299957 (analog with digit 1), A299970, A299982..A299988, A299969 (digit 0, 2..8, 9).

a(n,f=1,d=6,a=0,u=[a])={for(n=1,n,f&&if(f==1,print1(a","),write(f,n-1," "a));for(k=u[1]+1,oo,setsearch(u,k)&&next;setsearch(Set(digits(a+k)),d)&&(a=k)&&break);u=setunion(u,[a]);u[2]==u[1]+1&&u=u[^1]);a}

cp's OEIS Frontend

A299982 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 2, and no term occurs twice.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A299980 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 0, and no term occurs twice.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

A299981 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 1, and no term occurs twice.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

A299952 The sum a(n) + a(n+1) is a substring of the concatenation of all terms up to a(n+1). Lexicographic first sequence of positive integers without duplicate terms having this property.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A299978 Lexicographic first sequence of positive integers such that a(n) + a(n+1) has a digit 8, and no term occurs twice.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A299983 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 3, and no term occurs twice.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A299987 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 7, and no term occurs twice.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A299984 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 4, and no term occurs twice.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A299985 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 5, and no term occurs twice.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A299986 Lexicographic first sequence of nonnegative integers such that a(n) + a(n+1) has a digit 6, and no term occurs twice.

Views