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The s-inners or non-s-aints, numbers generated like the Aronson series from the letters, specifically the s, in a generating sentence, "S ain't the second, third, fourth, fifth . . . letter of this sentence.".
+10
4
1, 9, 31, 36, 98, 107, 156, 164, 210, 221, 266, 312, 358, 365, 407, 417, 461, 468, 510, 520, 548, 556, 564, 566, 571, 577, 587, 598, 608, 613, 618, 623, 630, 641, 651, 661, 671, 673, 680, 686, 698, 711, 723, 730, 735, 742, 749, 762, 792, 800, 846, 857, 905
COMMENTS
The discovery of the s-inners was inspired by the mention of the Aronson series in Douglas R. Hofstadter's Metamathematical Themas.
FORMULA
In blocks of 10 letters: saintthese condthirdf ourthfifth sixthseven theighthte nthelevent htwelfthth irteenthfo urteenthfi fteenthsix teenthseve nteentheig hteenthnin ...
EXAMPLE
a(1)= 1 because the first letter in the generating sentence that is s is the first one, a.
The p-est sequence is similar to the Aronson sequence except that instead of the generating sentence beginning with T, it begins with P and instead of being in English it is in Latin.
+10
1
1, 5, 10, 25, 40, 63, 84, 110, 135, 159, 192, 230, 265, 294, 330, 366, 397, 434, 455, 483, 523, 557, 598, 634, 645, 679, 717, 753, 795, 810, 832, 842, 856, 868, 898, 911, 938
REFERENCES
M. J. Halm, Newies, Mpossibilities 64, p. 3 (Mar. 1997)
FORMULA
From the generating sentence: "p est prima praeterea quinta praeterea decima praeterea quinta vicesima praeterea quadragesima praeterea tertia sexagesima praeterea quarta octogesima praeterea decima centesima ... littera in hic sententiam."
EXAMPLE
a(3) = 10 because the P in the first conjunction, praeterea, is the tenth in the generating sentence.
The t-est sequence is similar to the Aronson sequence except that instead of being in English it is in Latin.
+10
1
1, 4, 11, 16, 19, 29, 33, 42, 56, 70, 71, 74, 77, 87, 105, 109, 121, 128, 132, 142, 151, 161, 166, 171, 181, 185, 192, 202, 207, 212, 219, 227, 234, 251, 258, 261, 276, 283, 291, 313, 320, 343, 350, 366, 375, 382, 401, 408, 412, 427, 434, 443, 455, 462
REFERENCES
M. J. Halm, Newies, Mpossibilities 64, p. 3 (Mar. 1997)
FORMULA
From the generating sentence: "T est prima et quarta et undecima et sexima decima et nona decima et nona vicesima ... littera in hic sententiam."
EXAMPLE
a(2) = 4 because the T in the first use of the word, est, is the fourth in the generating sentence.
The n-est sequence is similar to the Aronson sequence except that instead of the generating sentence beginning with T, it begins with N and instead of being in English it is in Latin.
+10
0
1, 18, 24, 2753, 59, 62, 95, 98, 126, 132, 135, 149, 155, 170, 176, 184, 186, 191, 197, 212, 218, 221, 230, 251, 257, 260, 268, 271, 273, 289, 295, 298, 309, 311, 327, 333, 336, 356, 371, 377, 380, 389, 403, 418, 424, 427, 435, 449, 464, 470, 473, 478, 480
REFERENCES
M. J. Halm, Newies, Mpossibilities 64, p. 2 (Mar. 1997)
FORMULA
From the generating sentence: "N est prima littera in hic sententiam, doudevicesima littera in hic sententiam, quarta vicesima littera in hic sententiam, septima vicesima littera in hic sententiam, tertia quinquagentesima littera in hic sententiam ...."
EXAMPLE
a(2) = 18 because the N in the first use of the word, in, is the tenth in the generating sentence.
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