A330832 -id:A330832 - cp's OEIS frontend

A330833 a(n) = first prime factor p of the term A330832(n) = p*q.

2, 2, 3, 2, 5, 2, 3, 17, 2, 7, 41, 5, 59, 2, 71, 13, 89, 101, 2, 17, 131, 3, 167, 173, 23, 29, 293, 383, 5, 13, 43, 677, 701, 743, 17, 761, 773, 827, 839, 857, 911, 1091, 1097, 5, 1163, 1181, 1193, 1217, 73, 1373, 1427, 79, 1487, 1559, 1583, 83, 2, 1709, 1811, 1847, 1931, 1973, 2129, 2273, 2309, 2339, 2411, 2663, 2729, 2789, 2957

Offset: 1

Walter Kehowski, Jan 08 2020

			a(5) = 5 and, since A330834(5) = 3, then A330835(5) = (5^3-1)/(5-1) = 31 is prime.

Walter Kehowski, Table of n, a(n) for n = 1..4731

Cf. A003424, A023194, A023195, A085104, A330832, A330834, A330835.

A330834 The exponents k of A330832, that is, if A330832(n)=p*q, where p is prime and q=(p^k-1)/(p-1) is prime, then a(n)=k.

Original entry on oeis.org

2, 3, 3, 5, 3, 7, 7, 3, 13, 5, 3, 7, 3, 17, 3, 5, 3, 3, 19, 5, 3, 13, 3, 3, 5, 5, 3, 3, 11, 7, 5, 3, 3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 13, 3, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 5, 31, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Walter Kehowski, Jan 08 2020

nonn

			a(5) = 3, and, since A330833(5)=5, then A330835(5)=(5^3-1)/(5-1) = 31 is prime.

Walter Kehowski, Table of n, a(n) for n = 1..4731
G. Sobczyk, The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly 108(4), April 2001.

Cf. A003424, A023194, A023195, A085104, A330832, A330833, A330835.

A330835 Primes q appearing in A330832: that is, if A330832(n)=p*q, where p is prime and q=(p^k-1)/(p-1) is prime, then a(n)=q.

Original entry on oeis.org

3, 7, 13, 31, 31, 127, 1093, 307, 8191, 2801, 1723, 19531, 3541, 131071, 5113, 30941, 8011, 10303, 524287, 88741, 17293, 797161, 28057, 30103, 292561, 732541, 86143, 147073, 12207031, 5229043, 3500201, 459007, 492103, 552793, 25646167, 579883, 598303, 684757

Offset: 1

Walter Kehowski, Jan 08 2020

nonn

The terms in the b-file are the same as those of A003424 with y=1, but with an ordering based on that of A330832. The ordering allows the inclusion of the only duplicate 2^5-1=31 and (5^3-1)/(5-1)=31.

			a(5)=31 since A330833(5)=5, A330834(5)=3, and (5^3-1)/(5-1) = 31 is prime.

Walter Kehowski, Table of n, a(n) for n = 1..4731
G. Sobczyk, The Missing Spectral Basis in Algebra and Number Theory, The American Mathematical Monthly 108(4), April 2001.

Cf. A003424, A023194, A023195, A085104, A330832, A330833, A330834.

a(n) = (A330833(n) ^ A330834(n) - 1) / (A330833(n) - 1).

cp's OEIS Frontend

A330833 a(n) = first prime factor p of the term A330832(n) = p*q.

Views

Author

Keywords

Examples

Links

Crossrefs

A330834 The exponents k of A330832, that is, if A330832(n)=p*q, where p is prime and q=(p^k-1)/(p-1) is prime, then a(n)=k.

Views

Author

Keywords

Examples

Links

Crossrefs

A330835 Primes q appearing in A330832: that is, if A330832(n)=p*q, where p is prime and q=(p^k-1)/(p-1) is prime, then a(n)=q.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula