A159351 Smallest prime of the form a^2 + b^2 with 0 < a < b such that a + b = 2n+1.
5, 13, 29, 41, 61, 89, 113, 149, 181, 233, 269, 313, 389, 421, 521, 557, 613, 709, 761, 853, 929, 1013, 1109, 1201, 1301, 1409, 1553, 1637, 1741, 1861, 1997, 2113, 2269, 2381, 2521, 2677, 2837, 2969, 3121, 3461, 3449, 3613, 3797, 4001, 4153, 4337, 4513, 4729, 5081
Offset: 1
Keywords
Examples
1^2 + 2^2 = 5 = a(1) = 1. 2^2 + 3^2 = 13 = a(2) < 1^2 + 4^2 = 17. 2^2 + 5^2 = 29 = a(3) < 1^2 + 6^2 = 37. 23^2 + 32^2 = 1553 = a(27) < 1597, 1657, 1693, 1733, 1777, 1877, 1933, 1993, 2273, 2437, 2617, 2713, 2917, 14 prime representations as sum of two squares.
References
- L. E. Dickson, History of the Theory of Numbers, Vol, I: Divisibility and Primality, AMS Chelsea Publ., 1999
- R. K. Guy, Unsolved Problems in Number Theory (2nd ed.) New York: Springer-Verlag, 1994
- David Wells, Prime Numbers: The Most Mysterious Figures in Math. John Wiley and Sons. 2005
Programs
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PARI
isok(p, n) = for (i=1, 2*n, if (i^2 + (2*n+1-i)^2 == p, return (1));); 0; a(n) = {my(p = 2); while (! isok(p, n), p = nextprime(p+1)); p;} \\ Michel Marcus, Jan 29 2017
Extensions
A-number in definition and cross-reference corrected, and more terms from R. J. Mathar, Apr 24 2009
Edited by Thomas Ordowski, Jan 25 2017
Comments