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Lexicographically earliest sequence of distinct prime terms such that the English names of the entries form the sequence A000040 (the prime numbers). See how in the Comments section.
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4
5, 23, 22003, 11, 59, 3001, 7, 37, 101, 2, 41, 83, 29, 97, 3, 109, 19, 137, 223, 311, 71, 139, 31, 47, 149, 373, 13, 53, 163, 401, 67, 409, 367, 379, 197, 43, 113, 229, 257, 73, 107, 127, 151, 337, 199, 461, 499, 167, 233, 17, 503, 173, 313, 79, 331, 179, 103, 541, 577, 353, 569, 587, 227, 397, 263
COMMENTS
The first English names of the sequence are:
FIVE, TWENTY-THREE, TWENTY-TWO THOUSAND THREE, ELEVEN, FIFTY-NINE, THREE THOUSAND ONE, SEVEN, THIRTY-SEVEN, ONE HUNDRED ONE, TWO, FORTY-ONE, EIGHTY-THREE, TWENTY-NINE, NINETY-SEVEN, THREE, ONE HUNDRED NINE, NINETEEN, ...
If we now take the 5th letter of the above English sequence (T), the 23rd (W) and the 22003rd (O) we spell T.W.O. and 2 is the first term of A000040 (the prime numbers). We then take the 11th letter of the sequence (T), the 59th (H), the 3001st (R), the 7th (E) and the 37th (E) to form T.H.R.E.E. and 3 is the next term of A000040. The letters in position 101, 2, 41 and 83 will spell F.I.V.E. and 5 is the next term of A000040. Etc. This sequence is the lexicographically earliest permutation of A000040 with this property.
Lexicographically earliest sequence of distinct positive terms such that the English names of the entries form a new sequence of English names where every original entry is doubled (repetitions allowed, see the Comments section).
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2
5, 10, 20, 5, 9, 4, 7, 5, 13, 1, 23, 25, 5, 13, 5, 4, 7, 4, 2, 119, 800, 5, 4, 4, 7, 4, 2, 119, 36, 5, 1, 23, 24, 25, 5, 4, 4, 7, 5, 4, 7, 5, 9, 4, 7, 5, 13, 26, 2, 179, 5, 9, 23, 1, 23, 25, 5, 13, 26, 2, 179, 1, 2, 1, 5, 13, 5, 4, 7, 5, 9, 4, 7, 5, 13, 26, 2, 179, 5, 4, 7, 4, 2, 119, 36, 5, 1, 23, 24, 25, 5, 4, 4
COMMENTS
The first English names of the sequence are:
FIVE, TEN, TWENTY, FIVE, NINE, FOUR, SEVEN, FIVE, THIRTEEN, ONE, TWENTY-THREE, TWENTY-FIVE, FIVE, THIRTEEN, FIVE, FOUR, SEVEN, FOUR, TWO, ONE HUNDRED NINETEEN, EIGHT HUNDRED, FIVE, FOUR, FOUR, ...
If we now take the 5th letter of the above English sequence (T), the 10th (E) and the 20th (N) we spell T.E.N. and 10 is the double of a(1) = 5. We then take again the 5th letter of the sequence (T), the 9th (W), the 4th (E), the 7th (N), the 5th again (T), the 13th (Y) to form T.W.E.N.T.Y. and 20 is the double of a(2) = 10. Etc.
We are allowed to use the same letter many times (like the 4th one, E, for instance) to form a new name. The sequence A345711 forbids such repetitions. No obvious pattern appears in the sequence, although the set of names is limited.
Lexicographically earliest sequence such that the English names of the entries form the sequence A000040 (the prime numbers). See how in the Comments section.
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1
5, 12, 21, 40, 37, 39, 4, 4, 1, 2, 3, 4, 31, 4, 3, 4, 14, 4, 8, 4, 3, 4, 14, 5, 26, 2, 22, 5, 4, 4, 14, 31, 4, 3, 4, 14, 5, 4, 4, 14, 14, 2, 14, 4, 5, 4, 4, 14, 5, 6, 4, 14, 5, 16, 5, 26, 22, 4, 4, 5, 6, 4, 14, 5, 16, 14, 2, 14, 4, 5, 26, 2, 22, 5, 16, 17, 14, 4, 5, 26, 2, 22, 5, 16, 31, 4, 3, 4, 14, 1, 17, 22, 5
COMMENTS
The first English names of the sequence are:
FIVE, TWELVE, TWENTY-ONE, FORTY, THIRTY-SEVEN, THIRTY-NINE, FOUR, FOUR, ONE, TWO, THREE, FOUR, THIRTY-ONE, FOUR, THREE, FOUR, FOURTEEN, FOUR, EIGHT, FOUR, THREE, FOUR, FOURTEEN, FIVE, TWENTY-SIX, TWO, TWENTY-TWO,...
If we now take the 5th letter of the above English sequence (T), the 12th (W) and the 21st (O) we spell T.W.O. and 2 is the first term of A000040 (the prime numbers). We then take the 40th letter of the sequence (T), the 37th (H), the 39th (R), the 4th (E) and the 4th again (E) to form T.H.R.E.E. and 3 is the next term of A000040. The letters in position 1, 2, 3 and 4 will spell F.I.V.E. and 5 is the next term of A000040. Etc. We are allowed to use the same letter many times (like the 4th one, E, for instance) to form a new name. The sequence A345714 forbids such repetitions. No obvious pattern appears in the sequence, although the set of names is limited.
Lexicographically earliest sequence of prime terms such that the English names of the entries form the sequence A000040 (the prime numbers). See how in the Comments section.
+10
0
5, 23, 22003, 5, 53, 13, 7, 7, 83, 15013, 3, 7, 29, 7, 3, 7, 19, 7, 179, 7, 11003, 7, 19, 5, 53, 2, 13, 5, 7, 7, 19, 29, 7, 3, 7, 19, 5, 7, 7, 19, 19, 2, 19, 7, 5, 7, 7, 19, 5, 17, 7, 19, 5, 409, 70001, 53, 13, 7, 7, 5, 17, 7, 19, 5, 409, 19, 2, 19, 7, 5, 53, 2, 13, 5, 409, 389, 19, 7, 5, 53, 2, 13, 5, 409, 29, 7, 3, 7
COMMENTS
The first English names of the sequence are:
FIVE, TWENTY-THREE, TWENTY-TWO THOUSAND THREE, FIVE, FIFTY-THREE, THIRTEEN, SEVEN, SEVEN, EIGHTY-THREE, FIFTEEN THOUSAND THIRTEEN, THREE, SEVEN, TWENTY-NINE, SEVEN, THREE, SEVEN, NINETEEN, SEVEN, ONE HUNDRED SEVENTY-NINE, SEVEN, ELEVEN THOUSAND THREE, SEVEN, ...
If we now take the 5th letter of the above English sequence (T), the 23rd (W) and the 22003rd (O) we spell T.W.O. and 2 is the first term of A000040 (the prime numbers). We then take again the 5th letter of the sequence (T), the 53rd (H), the 13th (R), the 7th (E) and the 37th (E) to form T.H.R.E.E. and 3 is the next term of A000040. The letters in position 83, 15013, 3 and 7 will spell F.I.V.E. and 5 is the next term of A000040. Etc. We are allowed to use the same letter many times (like the 7th one, E, for instance) to form a new name. The sequence A345713 forbids such repetitions. No obvious pattern appears in the sequence, although the set of names is limited
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