

A157430


Primes of the form 9*(p^4)2 or 9*(p^4)+2, arising in PaleyHadamard difference sets.


0



727, 5623, 21611, 131771, 751691, 8311687, 16867447, 25431851, 71014331, 109056251, 350550731, 3170478247, 4435959611, 4678970407, 6353205851, 9659548091, 11977770247, 26525659687, 29365277771, 39262233611, 52986054967
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OFFSET

1,1


COMMENTS

Polhill is able to construct PaleyHadamard difference sets of the StantonSprott family in groups of the form (Z_3)^2 X (Z_p)^4t X (Z_(9p^4t)+2 or 2 when 9*(p^4t)2 or 9*(p^4t)+2 is a prime power. In this sequence, we are taking just the t=1 case, a prime power as first power of prime.


REFERENCES

John Bowen Polhill, Paley partial difference sets in groups with order not a prime power, 1046th Meeting of the AMS, Washington, DC, January 58, 2009.


LINKS

Table of n, a(n) for n=1..21.


EXAMPLE

a(1) = 9*(3^4)  2 = 727 is prime. a(2) = 9*(5^4)  2 = 5623 is prime. a(3) = 9*(7^4) + 2 = 21611. a(4) = 9*(11^4) + 2 = 131771. a(5) = 9*(17^4) + 2 = 751691. a(6) = 9*(31^4)  2 = 8311687. a(7) = 9*(37^4)  2 = 16867447. a(8) = 9*(41^4) + 2 = 25431851.


CROSSREFS

Sequence in context: A129117 A158394 A038600 * A215158 A178654 A094733
Adjacent sequences: A157427 A157428 A157429 * A157431 A157432 A157433


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Mar 01 2009


EXTENSIONS

More terms from R. J. Mathar, Mar 06 2009


STATUS

approved



