A261147 English flagpole sequence of nonnegative integers (like A215693, but with a(1)=0).

0, 1, 3, 2, 4, 7, 5, 8, 13, 14, 9, 10, 12, 20, 21, 15, 22, 24, 23, 6, 11, 17, 16, 18, 25, 19, 27, 26, 28, 29, 38, 30, 31, 32, 33, 34, 35, 36, 37, 39, 41, 40, 42, 44, 43, 45, 47, 48, 49, 51, 46, 57, 53, 50, 55, 59, 52, 62, 58, 111, 65, 61, 54, 72, 63, 67, 56

Offset

1,3

Comments

Concatenate the spelling of the terms in English (ignoring "and", punctuation, capitalization, and spaces); the i-th letter of this infinite word is in a(i). This is the lexicographically least such sequence of distinct nonnegative integers. A215693 is the lexicographically least such sequence of distinct positive integers.

In the first 100000 terms: the records for a(n)-n are set by a(1)=0, a(3)=3, a(6)=7, a(9)=13, a(14)=20, a(31)=38, a(60)=111, a(119)=211, a(18617)=18711; the records for n-a(n) are set by a(1)=0, a(4)=2, a(20)=6, a(335)=319.

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..3000

Wikipedia, English numerals

Hans Havermann, List of a(n) for n = 1..100000

Example

The sequence begins: 0,1,3,2,4,7,5,8,13....
The initial terms are spelled: ZERO;ONE;THREE;TWO;....
These letters are found in the spelling of the initial terms: Zero, onE, thRee, twO; fOur, seveN, fivE; eighT, tHirteen, ....

Prog

(Sage)
little = {0:"", 1:"one", 2:"two", 3:"three", 4:"four", 5:"five", 6:"six", 7:"seven", 8:"eight", 9:"nine", 10:"ten", 11:"eleven", 12:"twelve", 13:"thirteen", 14:"fourteen", 15:"fifteen", 16:"sixteen", 17:"seventeen", 18:"eighteen", 19:"nineteen"}
decade = {2:"twenty", 3:"thirty", 4:"forty", 5:"fifty", 6:"sixty", 7:"seventy", 8:"eighty", 9:"ninety"}
illion = {1:"thousand", 2:"million", 3:"billion", 4:"trillion"}
def nmb_wrd(n): # For positive integers n<10^15
    if n<20: return little[n]
    if n<100: return decade[floor(n/10)] + little[n%10]
    if n<1000: return little[floor(n/100)] + "hundred" + nmb_wrd(n%100)
    k = floor((len(str(n))-1)/3)
    return nmb_wrd(floor(n/10^(3*k))) + illion[k] + nmb_wrd(n%(10^(3*k)))
def English_fp(n, A = [0, 1, 3, 2], i = 1):
    while len(A)<n:
        for let in list(nmb_wrd(A[i])):
            new = 1
            while (new in A) or (let not in list(nmb_wrd(new))): new += 1
            A.append(new)
        i += 1
    return A[:n]
English_fp(67) # A215693 is English_fp(113, [1, 7, 3])

Crossrefs

Cf. A215693.

Sequence in context: A054086 A163329 A362978 * A212952 A246259 A105025

Adjacent sequences: A261144 A261145 A261146 * A261148 A261149 A261150

Keyword

nonn,word

Author

Danny Rorabaugh, Nov 28 2015

Extensions

Corrected by Danny Rorabaugh, Nov 29 2015

Status

approved