A175513 Numbers k for which 6k+1, 24k+5, 432k^2+72k-1, and 432k^2+90k-1 are all prime.

1, 2, 13, 753, 767, 1336, 1771, 1773, 1911, 2487, 3527, 4192, 5061, 5343, 5973, 6341, 7062, 7777, 8932, 9153, 15301, 17976, 18713, 19543, 20318, 22253, 24068, 27461, 29416, 29502, 31383, 31593, 31616, 31693, 36026, 36087, 41456, 42966, 44711, 45453, 45493, 46766, 49067, 50602, 51212, 51393, 53193, 56762, 58267, 60332, 60918, 64126, 65727, 67872, 71266, 72011, 75861, 78728, 79652, 82978, 85246, 86207, 86988, 87793, 90873, 91753, 94173, 97297

Offset

1,2

Comments

10368k^3+3888k^2+336k-5 is a Ruth-Aaron number (2, A039752).

References

C. Nelson, D. E. Penney and C. Pomerance, "714 and 715", J. Recreational Math. 7 (No. 2) 1974, 87-89.

Links

Table of n, a(n) for n=1..68.

Terrel Trotter, Jr., 1974 article providing the basis for this sequence (for defined variables s, p, q, r, replace x with 3k) [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - N. J. A. Sloane, Mar 29 2018]

Mathematica

Select[Range[100000], PrimeQ[6 # + 1] && PrimeQ[24 # + 5] && PrimeQ[432*#^2 + 72*# - 1] && PrimeQ[432 #^2 + 90 # - 1] &]
Select[Range[100000], AllTrue[{6#+1, 24#+5, 432#^2+72#-1, 432#^2+90#-1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 24 2019 *)

Crossrefs

Cf. A039752.

Sequence in context: A101342 A119122 A109947 * A064185 A069109 A004071

Adjacent sequences: A175510 A175511 A175512 * A175514 A175515 A175516

Keyword

nonn

Author

Hans Havermann, Dec 03 2010

Status

approved