A103946 Indices of icosahedral numbers (A006564) which are semiprimes.

37, 61, 157, 193, 229, 313, 373, 397, 409, 433, 457, 601, 613, 673, 877, 997, 1009, 1321, 1429, 1453, 1489, 1549, 1657, 1741, 1777, 1861, 2017, 2293, 2377, 2557, 2677, 2689, 2713, 2749, 2797, 2857, 2917, 2953, 3109, 3169, 3181, 3361, 3433, 3517, 4021

Offset: 1

Author

Jonathan Vos Post, Feb 20 2005

Keywords

• nonn
• easy

Examples

			a(69) = 7333 because the 69th icosahedral number to be a semiprime is A006564(7333) = 7333 * (5*73332 - 5*7333 + 2)/2 = 985657062703 = 7333 * 134413891, which is a term of A001358, a semiprime because both 7333 and 134413891 are primes.
		

References

• J. H. Conway and R. K. Guy, The Book of Numbers, New York, Springer-Verlag, p. 50, 1996.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.
• Eric Weisstein's World of Mathematics, Semiprime.

Crossrefs

Cf. A001222, A001358, A006564, A099186, A102294.

Programs

Mathematica

Select[ Prime[ Range[ 557]], PrimeQ[(5#^2 - 5# + 2)/2] &] (* Robert G. Wilson v, Feb 21 2005 *)

PARI

isok(n) = bigomega(n*(5*n^2 -5*n + 2)/2) == 2; \\ Michel Marcus, Dec 14 2015

Formula

Numbers k such that A006564(k) is a term of A001358.

Numbers k such that A102294(k) = 2.

Numbers k such that A001222(A006564(k)) = 2.

Numbers k such that Bigomega(k*(5*k^2 - 5*k + 2)/2) = 2.

Extensions

Edited and extended by Robert G. Wilson v, Feb 21 2005