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.

Showing 1-5 of 5 results.

A138535 Odd primes p_n for which A140140(n) < (p_n-1)/2, where p_n = n-th odd prime (A065091).

Original entry on oeis.org

13, 17, 31, 41, 61, 73, 89, 109, 113, 131, 151, 163, 193, 199, 211, 229, 233, 241, 281, 307, 313, 337, 379, 397, 401, 421, 461, 463, 521, 523, 541, 577, 593, 601, 613, 617, 631, 661, 673, 701, 727, 757, 761, 769, 811, 829, 859, 881, 883, 911, 937, 941, 953
Offset: 1

Views

Author

Vladimir Shevelev, May 10 2008

Keywords

Crossrefs

Cf. A140140, A137576, A065091, A138536.

Extensions

Corrected and extended by Ray Chandler, May 19 2008

A138786 "Left" odd composite numbers n for which n < A140607((n-1)/2).

Original entry on oeis.org

9, 21, 25, 27, 35, 45, 49, 55, 69, 75, 77, 81, 93, 95, 99, 105, 115, 119, 121, 125, 133, 135, 141, 143, 147, 153, 155, 161, 165, 169, 175, 187, 189, 203, 207, 209, 213, 215, 217, 219, 221, 225, 231, 235, 237, 243, 245, 247, 253, 259, 261, 267, 279, 285, 287
Offset: 1

Views

Author

Vladimir Shevelev, May 18 2008

Keywords

Comments

There are odd composite numbers which are neither in this sequence nor in A140608. The first such number is 91, see A140667.

Links

Crossrefs

Cf. A140607, A039649, A140140, A138193, A138217, A138227, A138535, A138536, A138537, A138539, A140141, A000010, A000040, A140608, A140667.

Extensions

Extended by Ray Chandler, May 20 2008

A140607 (A039649(2n+1)+A137576(n))/2.

Original entry on oeis.org

3, 5, 7, 10, 11, 13, 13, 17, 19, 22, 23, 31, 37, 29, 31, 31, 43, 37, 37, 41, 43, 55, 47, 64, 45, 53, 61, 55, 59, 61, 55, 61, 67, 78, 71, 73, 91, 106, 79, 136, 83, 77, 85, 89, 91, 96, 109, 97, 136, 101, 103, 109, 107, 109, 109, 113, 155, 103, 145, 166, 111, 201, 127, 113
Offset: 1

Views

Author

Vladimir Shevelev, May 18 2008

Keywords

Comments

If 2n+1 is a prime then a(n) = 2n+1.

Links

Crossrefs

Cf. A039649, A137576, A000010, A000040, A140140, A138193, A138217, A138227, A138535, A138536, A138537, A138539, A140141, A140608, A138786, A140667.

Extensions

Extended by Ray Chandler, May 20 2008, May 24 2008

A140608 "Right" odd composite numbers n for which n > A140607((n-1)/2).

Original entry on oeis.org

15, 33, 39, 51, 57, 63, 65, 85, 87, 111, 117, 123, 129, 145, 159, 171, 177, 183, 185, 195, 201, 205, 249, 255, 265, 273, 275, 291, 303, 305, 315, 321, 327, 333, 339, 341, 393, 399, 411, 417, 435, 447, 451, 455, 465, 471, 481, 485, 489, 505, 511, 513, 519, 537
Offset: 1

Views

Author

Vladimir Shevelev, May 18 2008

Keywords

Comments

Conjecture. The sequence is infinite.

Links

Crossrefs

Cf. A140607, A039649, A140140, A138193, A138217, A138227, A138535, A138536, A138537, A138539, A140141, A000010, A000040, A138786, A140667.

Extensions

Extended by Ray Chandler, May 20 2008

A140667 Odd composite numbers k for which k = A140607((k-1)/2).

Original entry on oeis.org

91, 1581, 2465, 8481, 25761, 31609, 33355, 34945, 118405, 146611, 319507, 736291, 994507, 3270403, 3375487, 5176153, 6186403, 6228685, 8650951, 10679131, 22028203, 26017291, 31470211, 33796531, 41710411, 42149971, 42474547, 46672291, 48316969, 49019851, 58986091, 68182003, 69885649
Offset: 1

Views

Author

Ray Chandler, May 20 2008

Keywords

Crossrefs

Cf. A140607, A039649, A140140, A138193, A138217, A138227, A138535, A138536, A138537, A138539, A140141, A000010, A000040, A140608, A138786.

Programs

  • PARI
    f(n) = (eulerphi(2*n+1) + 1 + g(n))/2; \\ A140607
g(n) = sumdiv(2*n+1, d, eulerphi(d)/(t=znorder(Mod(2, d))))*t-t+1; \\ A137576
isok(c) = if (!isprime(c) && (c%2), f((c-1)/2) == c); \\ Michel Marcus, Jan 31 2023

Extensions

More terms from Michel Marcus, Jan 31 2023
Showing 1-5 of 5 results.

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