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A175513 Numbers k for which 6k+1, 24k+5, 432k^2+72k-1, and 432k^2+90k-1 are all prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 19 19:30 EST 2020. Contains 332047 sequences. (Running on oeis4.)