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A122710 Primes of the form p^2 + q^8 where p and q are primes. 1
281, 617, 1097, 1217, 5297, 10457, 17417, 19577, 23057, 32297, 39857, 44777, 52697, 58337, 72617, 167537, 192977, 212777, 241337, 249257, 383417, 398417, 502937, 517217, 564257, 704177, 830177, 885737, 943097, 982337, 1018337, 1038617, 1079777, 1442657, 1515617, 1560257, 1692857, 1745297, 1985537 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

p and q cannot both be odd. Thus p=2 or q=2. There are no primes of the form 2^2 + q^8 (consider divisibility by 5). Hence all solutions are of the form p^2 + 2^8 and are congruent to 7 mod 10.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

{a(n)} = {p^2 + q^8 in A000040 where p and q are in A000040}.

EXAMPLE

a(1) = 5^2 + 2^8 = 281.

a(2) = 19^2 + 2^8 = 617.

a(3) = 29^2 + 2^8 = 1097.

MAPLE

N:= 10^6: # to get terms up to N

select(isprime, [seq(2^8 + p^2, p = select(isprime, [5, seq(seq(10*i+j, j=[1, 9]), i=1..isqrt(N-2^8)/10)]))]); # Robert Israel, Jan 24 2018

CROSSREFS

Cf. A000040, A045700 (of form p^2+q^3), A122617 (of form p^3+q^4).

Sequence in context: A142397 A142546 A163184 * A161191 A108836 A295983

Adjacent sequences:  A122707 A122708 A122709 * A122711 A122712 A122713

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Sep 23 2006

EXTENSIONS

More terms from Robert Israel, Jan 24 2018

STATUS

approved

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Last modified April 13 10:52 EDT 2021. Contains 342935 sequences. (Running on oeis4.)