A281067 -id:A281067

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A281068

a(1) = 1. a(n) is the smallest natural number that is not already in the sequence such that the name of a(n) in English starts with the letter a(n-1) ends with, and a(n) makes the sequence extendable.

+10
3

1, 8, 2, 101, 11, 9, 18, 19, 91, 81, 82, 102, 103, 83, 85, 87, 92, 105, 88, 3, 89, 801, 802, 107, 93, 803, 805, 807, 95, 808, 10, 97, 98, 12, 809, 810, 99, 811, 901, 812, 813, 902, 108, 13, 903, 814, 905, 815, 907, 908, 21, 816, 909, 817, 910, 911, 912, 818, 913, 914, 915, 916, 917, 918, 919

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

"a(n) makes the sequence extendable" means the name of a(n) does not end with any of the letters r, x, y and d.

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

If a(4) were 100 (one hundred, which ends with d), it would make the sequence finite. Therefore, a(4) has to be 101.

CROSSREFS

Cf. A277971, A277972, A281067.

KEYWORD

easy,nonn,word

AUTHOR

Ivan N. Ianakiev, Jan 14 2017

STATUS

approved

A282636

a(1) = 1. a(n) is the smallest natural number such that a(n) > a(n-1), the name of a(n) in (American) English ends with the letter a(n-1) starts with, and a(n) makes the sequence extendable.

+10
1

1, 2, 8, 9, 10, 28, 38, 88, 89, 91, 97, 107, 122, 132, 142, 152, 162, 172, 182, 192, 202, 208, 228, 238, 248, 258, 268, 278, 288, 298, 308, 328, 338, 348, 358, 368, 378, 388, 398, 808, 809, 812, 821, 823, 825, 829, 831, 833, 835, 839, 841, 843, 845, 849, 851, 853, 855, 859

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

"a(n) makes the sequence extendable" means the name of a(n) does not start with any of the letters f and s.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

38 is followed by 88 as 48, 58, 68 and 78 cannot make the sequence extendable.

MATHEMATICA

names = StringReplace[

IntegerName /@ Range[1000], {"\[Hyphen]" -> "", " " -> ""}];

lst = {1}; next[n_] := next[n] =

Module[{pos = Last[lst] + 1},

While[

Or[

And[First[Characters[names[[Last[lst]]]]] !=

Last[Characters[names[[pos]]]], pos <= Length[names]],

MemberQ[{"f", "s"}, First[Characters[names[[pos]]]]] == True

pos++

];

AppendTo[lst, pos]

];

seq[n_] := Nest[next, 1, n]; seq[57]

CROSSREFS

Cf. A277971, A277972, A281067, A281068, A282637.

KEYWORD

easy,nonn,word

AUTHOR

Ivan N. Ianakiev, Feb 20 2017

STATUS

approved

A282637

a(1) = 1. a(n) is the smallest unlisted natural number whose name in (American) English ends with the letter a(n-1) starts with, and makes the sequence extendable.

+10
1

1, 2, 8, 3, 28, 38, 88, 9, 10, 98, 11, 12, 108, 22, 128, 32, 138, 82, 21, 148, 92, 13, 158, 102, 122, 132, 142, 152, 162, 172, 182, 192, 202, 168, 222, 178, 232, 188, 242, 198, 252, 208, 228, 238, 248, 258, 268, 278, 288, 298, 308, 328, 338, 348, 358, 368, 378, 388, 398, 808, 23, 828, 25, 838, 29, 848

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

"a(n) ... makes the sequence extendable" means the name of a(n) does not start with any of the letters f and s.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

38 is followed by 88 as 48, 58, 68 and 78 cannot make the sequence extendable.

MATHEMATICA

names = StringReplace[

IntegerName /@ Range[1000], {"\[Hyphen]" -> "", " " -> ""}];

lst = {1}; next[n_] := next[n] =

Module[{pos = Complement[Range[Length[names]], lst], i = 1},

While[

Or[

And[

First[Characters[names[[Last[lst]]]]] != Last[Characters[names[[pos[[i]]]]]],

pos[[i]] <= Length[names]

MemberQ[{"f", "s"}, First[Characters[names[[pos[[i]]]]]]] == True

i++

];

AppendTo[lst, pos[[i]]]

];

seq[n_] := Nest[next, 1, n]; seq[65]

CROSSREFS

Cf. A277971, A277972, A281067, A281068, A282636.

KEYWORD

easy,nonn,word

AUTHOR

Ivan N. Ianakiev, Feb 20 2017

STATUS

approved

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