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 1-3 of 3 results.

A144326 Prime numbers that cannot be Mersenne prime exponents, by conjecture of A144325.

Original entry on oeis.org

67, 191, 197, 211, 277, 331, 379, 397, 401, 541, 617, 631, 677, 727, 743, 751, 821, 937, 947, 971, 991, 1129, 1163, 1171, 1217, 1277, 1289, 1327, 1381, 1409, 1427, 1471, 1549, 1559, 1597, 1601, 1607, 1783, 1801, 1831, 1871, 1901, 2011, 2017, 2081, 2111
Offset: 1

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Author

Reikku Kulon, Sep 17 2008

Keywords

Comments

Obviously true for the initial terms!
Conjecture: 191, 1217, 1559 and 1901 are not in fact members of this sequence, noting that they are (4, 19) k-figurate numbers; 19 is a member of A138694. Determining whether a Mersenne prime exponent one greater than a (4, 19) k-figurate number exists is sufficient to determine whether these primes are members.

Crossrefs

Cf. A000040, A000043, A000668, A144313, A144315, A144325, A138694

A144715 A144325(n) + A144313(n) + A144315(n).

Original entry on oeis.org

275, 431, 587, 1115, 1271, 2309, 2891, 3203, 3725, 4421, 4787, 5453, 6017, 6257, 6599, 6797, 7295, 7841, 8507, 8735, 8975, 9233, 9557, 9983, 10733, 11327, 11939, 12875, 13031, 13439, 14285, 15113, 15383, 15665, 16307, 17129, 17849, 18461
Offset: 1

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Author

Reikku Kulon, Sep 19 2008

Keywords

Comments

All terms are congruent to 5 modulo 6: A144325(n) and A144313(n) are each congruent to 5 and A144315(n) is congruent to 1.
None of the given terms have more than three distinct prime factors and most have only two. Several are primes.
The multiples of five are all fifth figurate numbers corresponding to polygons having a number of sides k = floor(a(n) / 10) + 2. 3725 = 5 * 5 * 149 is also the 50th pentagonal number. The rest are not figurates, except for 15113 = 7 * 17 * 127, which is the seventeenth 113-figurate number.

Crossrefs

Cf. A144325, A144313, A144315, A000326

A144716 (A144325(n)^2 + A144313(n)^2 + A144315(n)^2) / 3.

Original entry on oeis.org

10817, 25153, 45969, 158377, 206313, 855113, 1379273, 1573833, 2233913, 3101849, 3663737, 4880169, 5446849, 5795377, 6374833, 6710249, 7788217, 8673409, 10280489, 10737713, 11401337, 11917969, 12744377, 13922289, 16282793
Offset: 1

Views

Author

Reikku Kulon, Sep 19 2008

Keywords

Crossrefs

Cf. A144325, A144313, A144315
Showing 1-3 of 3 results.

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