proposed

approved

editing

proposed

Select[ Ceiling@ Im@ ZetaZero@ Range@ 600, 340, PrimeQ] (* Robert G. Wilson v, Jan 27 2015 *)

Select[ Ceiling@ Im@ ZetaZero@ Range@ 600, PrimeQ] (* Robert G. Wilson v, Jan 27 2015 *)

approved

editing

_Jani Melik (jani.melik(AT)gmail.com), _, May 20 2008

Multiplicative suborder of 4 (mod 2n+1) = sord(4, 2n+1).

Smallest integer greater than or equal to imaginary part of zeros of Riemann zeta function which is prime.

0, 1, 1, 3, 3, 5, 3, 2, 2, 9, 3, 11, 5, 9, 7, 5, 5, 6, 9, 6, 5, 7, 6, 23, 21, 4, 13, 10, 9, 29, 15, 3, 3, 33, 11, 35, 9, 10, 15, 39, 27, 41, 4, 14, 11, 6, 5, 18, 12, 15, 25, 51, 6, 53, 9, 18, 7, 22, 6, 12, 55, 10, 25, 7, 7, 65, 9, 18, 17, 69, 23, 30, 7, 21, 37, 15, 12, 10, 13, 26, 33, 81, 10

31, 41, 53, 61, 73, 83, 89, 139, 151, 151, 157, 179, 193, 197, 199, 257, 277, 283, 311, 313, 337, 347, 367, 379, 389, 397, 409, 419, 421, 431, 433, 439, 443, 457, 461, 463, 467, 479, 479, 487, 499, 503, 509, 521, 523, 541, 541, 557, 563, 569, 571, 587, 593

0,4

1,1

a(n) is minimum e for which 4^e = +/-1 mod 2n+1, or zero if no e exists. a(0) is the only zero in the sequence.

H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3

H. J. Smith, Andrew Michael Odlyzko, <a href="http://www.geocitiesdtc.umn.comedu/~odlyzko/hjsmithhzeta_tables/downloadindex.html#XICalc">XICalc - Extra Precision Integer Calculator.Tables of zeros of the Riemann zeta function</a>.

E. W. Weisstein, <a href="http://mathworld.wolfram.com/MultiplicativeOrder.html">Link to a section of The World of Mathematics</a>, Multiplicative Order.

S. Wolfram, <a href="http://www.stephenwolfram.com/publications/articles/ca/84-properties/9/text.html">Algebraic Properties of Cellular Automata (1984)</a>, Appendix B.

a(1)= 31. 4th zero of Riemann zeta function is 30.424876126... and the smallest integer greater or equal which is prime is 31.

Cf. A002410, A013629.

easy,nonn,new

nonn

Harry J. Smith Jani Melik (hjsmithhjani.melik(AT)sbcglobalgmail.netcom), Feb 11 2005May 20 2008

Cf. A002326 A002329 A050975-A050981 A070676-A070683 Adjacent sequences: A103488-A103498.

easy,nonn,new

Multiplicative suborder of 4 (mod 2n+1) = sord(4, 2n+1).

0, 1, 1, 3, 3, 5, 3, 2, 2, 9, 3, 11, 5, 9, 7, 5, 5, 6, 9, 6, 5, 7, 6, 23, 21, 4, 13, 10, 9, 29, 15, 3, 3, 33, 11, 35, 9, 10, 15, 39, 27, 41, 4, 14, 11, 6, 5, 18, 12, 15, 25, 51, 6, 53, 9, 18, 7, 22, 6, 12, 55, 10, 25, 7, 7, 65, 9, 18, 17, 69, 23, 30, 7, 21, 37, 15, 12, 10, 13, 26, 33, 81, 10

0,4

a(n) is minimum e for which 4^e = +/-1 mod 2n+1, or zero if no e exists. a(0) is the only zero in the sequence.

H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3

H. J. Smith, <a href="http://www.geocities.com/hjsmithh/download.html#XICalc">XICalc - Extra Precision Integer Calculator.</a>

E. W. Weisstein, <a href="http://mathworld.wolfram.com/MultiplicativeOrder.html">Link to a section of The World of Mathematics</a>, Multiplicative Order.

S. Wolfram, <a href="http://www.stephenwolfram.com/publications/articles/ca/84-properties/9/text.html">Algebraic Properties of Cellular Automata (1984)</a>, Appendix B.

Cf. A002326 A002329 A050975-A050981 A070676-A070683 Adjacent sequences: A103488-A103498.

easy,nonn,new

Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 11 2005

approved