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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 (list; graph; refs; listen; history; text; internal format)
 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 Robert Israel, Table of n, a(n) for n = 1..10000 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 Cf. A000040, A000583, A030514, A094479, A192926. Sequence in context: A362321 A130833 A130873 * A094479 A096326 A216380 Adjacent sequences: A193408 A193409 A193410 * A193412 A193413 A193414 KEYWORD nonn AUTHOR Jonathan Vos Post, Jul 25 2011 EXTENSIONS a(7)-a(33) from Charles R Greathouse IV, Jul 25 2011 STATUS approved

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Last modified August 2 21:27 EDT 2024. Contains 374875 sequences. (Running on oeis4.)