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

Author

Hans Havermann, Dec 03 2010

Keywords

• nonn

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

• Terrel Trotter, Jr., 1974 article providing the basis for this sequence (for defined variables s, p, q, r, replace x with 3k)

Crossrefs

Cf. A039752.

Programs

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 *)