cp's OEIS Frontend

A318530 Numbers that can be written in more than one way as p^2 + q^3 + r^4 with p, q and r primes.

%I A318530 #10 Jan 31 2019 03:31:00
%S A318530 145,210,637,754,2317,2530,2917,5218,5437,5890,6447,6997,7469,7653,
%T A318530 7738,8650,9333,11818,12417,12796,14770,15178,15197,15295,15513,16349,
%U A318530 16501,17367,18389,19709
%N A318530 Numbers that can be written in more than one way as p^2 + q^3 + r^4 with p, q and r primes.
%H A318530 Robert Israel, <a href="/A318530/b318530.txt">Table of n, a(n) for n = 1..10000</a>
%e A318530 a(1) = 145 = 2^2 + 5^3 + 2^4 = 11^2 + 2^3 + 2^4 .
%e A318530 The first term which can be written in three different ways is
%e A318530 17367 = 23^2 + 13^3 + 11^4 = 113^2 + 13^3 + 7^4 = 131^2 + 5^3 + 3^4 .
%p A318530 N:= 10^5: # to get terms <= N
%p A318530 P:= select(isprime, [2,seq(i,i=3..floor(sqrt(N)))]):
%p A318530 Psq:= map(`^`,P,2):
%p A318530 P3:= select(`<=`,map(`^`,P,3),N):
%p A318530 P4:= select(`<=`,map(`^`,P,4),N):
%p A318530 V:= Vector(N):
%p A318530 for a in Psq do for b in P3 do for c in P4 do
%p A318530    s:= a+b+c;
%p A318530    if s <= N then V[s]:= V[s]+1 fi
%p A318530 od od od:
%p A318530 select(t -> V[t]>=2, [$1..N]); # _Robert Israel_, Jan 30 2019
%Y A318530 Subset of A134657.
%K A318530 nonn
%O A318530 1,1
%A A318530 _Philippe Guglielmetti_, Aug 28 2018