cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A333788 Semiprimes whose both factors are Fermat primes.

Original entry on oeis.org

9, 15, 25, 51, 85, 289, 771, 1285, 4369, 66049, 196611, 327685, 1114129, 16843009, 4295098369
Offset: 1

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Author

Antti Karttunen, Apr 15 2020

Keywords

Comments

Product of two, not necessarily distinct Fermat primes.
For the finiteness or non-finiteness of this sequence, see A019434.
Most terms are binary palindromes (in A006995), except among the fifteen known terms, these squares > 9 are not: 25, 289, 66049, 4295098369.

Crossrefs

Subsequence of A334102.

A335912 Numbers k for which A335885(k) = 2.

Original entry on oeis.org

9, 11, 13, 15, 18, 19, 21, 22, 23, 25, 26, 29, 30, 35, 36, 38, 41, 42, 44, 46, 47, 49, 50, 51, 52, 58, 60, 61, 67, 70, 72, 76, 79, 82, 84, 85, 88, 92, 93, 94, 97, 98, 100, 102, 104, 113, 116, 119, 120, 122, 134, 137, 140, 144, 152, 155, 158, 164, 168, 170, 176, 184, 186, 188, 191, 193, 194, 196, 200, 204, 208, 217, 223
Offset: 1

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Author

Antti Karttunen, Jun 30 2020

Keywords

Comments

Numbers n such that when we start from k = n, and apply in some combination the nondeterministic maps k -> k - k/p and k -> k + k/p, (where p can be any of the odd prime factors of k), then for some combination we can reach a power of 2 in exactly two steps (but with no combination allowing 0 or 1 steps).

Examples

			For n = 70 = 2*5*7, if we first take p = 7 and apply the map n -> n + (n/p), we obtain 80 = 2^4 * 5. We then take p = 5, and apply the map n -> n - (n/p), to obtain 80-16 = 64 = 2^16. Thus we reached a power of 2 in two steps (and there are no shorter paths), therefore 70 is present in this sequence.
For n = 769, which is a prime, 769 - (769/769) yields 768 = 3 * 256. For 768 we can then apply either map to obtain a power of 2, as 768 - (768/3) = 512 = 2^9 and 768 + (768/3) = 1024 = 2^10. On the other hand, 769 + (769/769) = 770 and A335885(770) = 4, so that route would not lead to any shorter paths, therefore 769 is a term of this sequence.
		

Crossrefs

Row 2 of A335910.
Subsequences of semiprimes (union gives all odd semiprimes present): A144482, A333788, A336115.

Programs

A359585 Positions of even terms in A329697.

Original entry on oeis.org

1, 2, 4, 7, 8, 9, 11, 13, 14, 15, 16, 18, 22, 25, 26, 28, 30, 32, 36, 41, 43, 44, 47, 49, 50, 51, 52, 56, 57, 59, 60, 63, 64, 67, 69, 71, 72, 77, 79, 81, 82, 85, 86, 87, 88, 91, 93, 94, 95, 97, 98, 99, 100, 102, 104, 105, 107, 109, 111, 112, 114, 115, 117, 118, 120, 121, 126, 128, 131, 134, 135, 137
Offset: 1

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Author

Antti Karttunen, Jan 07 2023

Keywords

Comments

Numbers that occur on even-indexed rows of array A334100.

Crossrefs

Positions of +1's in A359581, positions of 0's in A359583.
Cf. A329697, A334100, A359584 (complement).
Cf. A000079, A334102, A334104, A334106 (subsequences).

Programs

A336122 Numbers k for which A335884(k) = 2.

Original entry on oeis.org

5, 7, 9, 10, 14, 18, 20, 28, 36, 40, 56, 72, 80, 112, 144, 160, 224, 288, 320, 448, 576, 640, 896, 1152, 1280, 1792, 2304, 2560, 3584, 4608, 5120, 7168, 9216, 10240, 14336, 18432, 20480, 28672, 36864, 40960, 57344, 73728, 81920, 114688, 147456, 163840, 229376, 294912, 327680, 458752, 589824, 655360, 917504, 1179648, 1310720
Offset: 1

Views

Author

Antti Karttunen, Jul 09 2020

Keywords

Comments

Numbers n such that when we start from k = n, and apply in any combination the nondeterministic maps k -> k - k/p and k -> k + k/p, (where p can be any of the odd prime factors of k), a power of 2 will appear no later than after two such steps, and on some of the combinations a power of 2 will appear after exactly two steps.

Crossrefs

Cf. A335884.
Cf. also A334102, A335882, A335912.

Programs

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