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

1,1

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), ...

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A235413 A238255 A210375 * A293858 A258547 A211573

Adjacent sequences: A173557 A173558 A173559 * A173561 A173562 A173563

Keyword

nonn

Author

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

Status

approved