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A193411
Primes which are sums of two or more distinct 4th powers of primes.
3
97, 641, 2417, 14657, 17123, 17683, 43283, 46309, 83537, 112163, 126739, 129221, 129749, 130337, 145043, 145603, 173539, 176021, 176549, 214483, 216259, 229189, 242419, 243109, 244901, 257141, 279857, 280547, 294563, 295123, 297589, 310819, 325541, 365779
OFFSET
1,1
COMMENTS
Primes in A130833. Primes which are sums of exactly two distinct 4th powers of primes must be in A094479 primes of the form p^4 + 16 where p is also a prime.
The first term that arises in more than one way is 6625607 = 2^4+5^4+7^4+11^4+17^4+23^4+41^4+43^4 = 2^4+5^4+7^4+13^4+17^4+29^4+31^4+47^4. - Robert Israel, Apr 27 2020
LINKS
EXAMPLE
a(5) = 17123 = 3^4 + 7^4 + 11^4.
MAPLE
N:= 5*10^5: # for all terms <= N
S1:= {}:
S2:= {}:
p:= 1:
R:= {}:
do
p:= nextprime(p);
if p^4 > N then break fi;
s:= p^4;
nS2:= select(`<=`, map(`+`, S1 union S2, s), N);
S2:= S2 union nS2;
S1:= S1 union {s};
R:= R union select(isprime, nS2);
od:
sort(convert(R, list)); # Robert Israel, Apr 27 2020
MATHEMATICA
nn = 9; Select[Sort[Table[Dot[IntegerDigits[i, 2, nn], Prime[Range[nn]]^4], {i, 2^nn-1}]], # < Prime[nn-1]^4 + Prime[nn]^4 && PrimeQ[#] &] (* T. D. Noe, Jul 27 2011 *)
PROG
(PARI) list(lim)=my(v=List(), t1, t2, t3, t4, t5, t6, t7); forprime(p=2, (lim-16)^(1/4), forprime(q=2, min(p-1, (lim-p^4)^(1/4)), t1=p^4+q^4; if(isprime(t1), listput(v, t1)); forprime(r=2, min(q-1, (lim-t1)^(1/4)), t2=t1+r^4; if(isprime(t2), listput(v, t2)); forprime(s=2, min(r-1, (lim-t2)^(1/4)), t3=t2+s^4; if(isprime(t3), listput(v, t3)); forprime(t=2, min(s-1, (lim-t3)^(1/4)), t4=t3+t^4; if(isprime(t4), listput(v, t4)); forprime(u=2, min(t-1, (lim-t4)^(1/4)), t5=t4+u^4; if(isprime(t5), listput(v, t5)); forprime(w=2, min(u-1, (lim-t5)^(1/4)), t6=t5+w^4; if(isprime(t6), listput(v, t6)); forprime(x=2, min(w-1, (lim-t6)^(1/4)), t7=t6+x^4; if(isprime(t7), listput(v, t7)); if(x>2&&t7+16<=lim&&isprime(t7+16), listput(v, t7+16)))))))))); vecsort(Vec(v), , 8);
list(4044955) \\ Charles R Greathouse IV, Jul 27 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Jul 25 2011
EXTENSIONS
a(7)-a(33) from Charles R Greathouse IV, Jul 25 2011
STATUS
approved