A173560 Numbers m such that (6*m)^5 is a sum of a twin prime pair.

16, 44, 84, 135, 161, 631, 849, 880, 1035, 1086, 1721, 1815, 2155, 2704, 2871, 2975, 3011, 3159, 3220, 3365, 3390, 3669, 3996, 4075, 4704, 4761, 5025, 5090, 5299, 5585, 5640, 5970, 6314, 6606, 7035, 7785, 8104, 8129, 8610, 9116, 9665, 9966, 10249

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 21 2010

Keywords

• nonn

Comments

The twin prime pairs are characterized in A173255.

No such m has least significant digit (LSD) e = 2 or 7 because a = (6 * e)^5/2 - 1, representing the smaller of the twin primes, would get LSD 5.

No such m has LSD e = 3 or 8, because a+2 = (6 * e)^5/2 + 1, representing the larger prime, would get LSD 5.

The primes in this sequence here are a(6) = 631 = prime(115), a(11) = 1721 = prime(268),

a(17) = 3011 = prime(432), a(49) = 10859 = prime(1320), ...

Examples

			p = (6 * 16)^5/2 - 1 = 4076863487 = A000040(193435931); p+2 = A000040(193435932), so a(1) = 16.
p = (6 * 44)^5/2 - 1 = 641194278911 = A000040(24524572848); p+2 = A000040(24524572849), so a(2) = 44.
p = (6 * 84)^5/2 - 1 = 16260080320511 = A000040(553382827197); p+2 = A000040(553382827198), so a(3) = 84.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A001359, A061308, A069496, A172271, A172494, A173255.

Programs

Mathematica

Select[Range[700],AllTrue[((6*#)^5-2)/2+{0,2},PrimeQ]&] (* Harvey P. Dale, Dec 21 2024 *)

PARI

isok(m) = {my(k = (6*m)^5/2); isprime(k-1) && isprime(k+1);} \\ Amiram Eldar, Jul 19 2025