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A097963 ["comma"], is the first, fifteenth, twenty-sixth, fortieth, ... character in this sentence, including spaces and punctuations. 1

%I #13 Aug 31 2021 04:09:43

%S 1,15,26,40,50,60,70,82,97,113,137,165,190,213,237,265,290,313,339,

%T 367,396,424,452,479,507,529,556,582,610,629,655,680,703,724,753,780,

%U 805,826,854,882,911,934,962,989,1016,1040,1063,1089,1116,1152,1191,1230

%N ["comma"], is the first, fifteenth, twenty-sixth, fortieth, ... character in this sentence, including spaces and punctuations.

%C Yes, the definition begins with a comma!

%H Jon E. Schoenfield, <a href="/A097963/b097963.txt">Table of n, a(n) for n = 1..1000</a>

%F After a(2) = 15, the remaining terms are given by the recursion a(n+1) = a(n) + 2 + length(OrdinalName(a(n))); e.g., a(3) = a(2) + 2 + length(OrdinalName(a(2))) = 15 + 2 + length("fifteenth") = 15 + 2 + 9 = 26. - _Jon E. Schoenfield_, Aug 13 2007

%e Label the coordinates:

%e 00000000011111111112222222222333333333344444444445...

%e 12345678901234567890123456789012345678901234567890... Then (comma)

%e ["Comma"], is the first, fifteenth, twenty-sixth, fortieth, fiftieth, fifty-ninth, seventy-second, eighty-eighth, one hundred third, one hundred twenty-second, ... character.

%o (Python)

%o from itertools import accumulate, repeat

%o from num2words import num2words

%o A097963_list = [1]+list(accumulate(repeat(15,100), lambda x, _: x+2+len(num2words(x,to='ordinal').replace(' and ',' ').replace(', ',' ')))) # _Chai Wah Wu_, Aug 30 2021

%Y Cf. A055508, A005224, A049525.

%K nonn,base,nice,easy,word

%O 1,2

%A _Ray G. Opao_, Sep 21 2004

%E Corrected and extended by _Jon E. Schoenfield_, Aug 13 2007

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Last modified August 10 19:25 EDT 2024. Contains 375058 sequences. (Running on oeis4.)