1,1

Tested up to n=10000000. Is this sequence finite?

n=4 -> Sum primes: 2+3=5: sum nonprimes: 1+4=5 -> 5/5=1.

n=21 -> Sum primes: 2+3+5+7+11+13+17+19=77: sum nonprimes: 1+4+6+8+9+10+12+14+15+16+18+20+21=154 -> 154/77=2.

n=24 -> Sum primes: 2+3+5+7+11+13+17+19+23=100;

Sum nonprimes: 1+4+6+8+9+10+12+14+15+16+18+20+21+22+24=200 -> 200/100=2.

n=71 -> Sum primes: 2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71=639;

Sum nonprimes: 1+4+6+8+9+10+12+14+15+16+18+20+21+22+24+25+26+27+28+30+32+33+34+35+36+38+39+40+42+44+45+46+48+49+50+51+52+54+55+56+57+58+60+62+63+64+65+66+68+69+70=1917 -> 1917/639=3.

P:=proc(n) local i, snp, sp; snp:=1; sp:=2; for i from 3 by 1 to n do if isprime(i) then sp:=sp+i; else snp:=snp+i; fi; if trunc(snp/sp)=snp/sp then print(i); fi; od; end: P(10000000);

Cf. A007504, A051349.

Sequence in context: A128452 A076943 A138228 this_sequence A041821 A042429 A086474

Adjacent sequences: A133781 A133782 A133783 this_sequence A133785 A133786 A133787

more,nonn

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jan 21 2008