A284102 Numbers that are the sum of 10 consecutive primes and also the sum of 10 consecutive semiprimes.
6504, 12946, 12990, 19052, 19764, 21490, 31638, 35604, 41300, 42364, 45212, 52528, 58104, 60034, 63400, 66662, 67858, 69880, 74090, 74824, 78542, 88844, 96256, 96346, 97818, 104584, 106970, 111122, 113120, 117540, 125384
Offset: 1
Keywords
Examples
a(1)=6504 because 6504 is the sum of 10 consecutive primes A000040(114..114+9)={619,631,641,643,647,653,659,661,673,677} and also
6504 is the sum of 10 consecutive semiprimes A001358(192..192+9)={629,633,634,635,649,655,662,667,669,671}.
Note that a(1) = 6504 = A283873(10).
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
-
Maple
N:= 10^6: P:= select(isprime, [$1..N]): S:= select(t -> numtheory:-bigomega(t)=2, [$1..N]): P10:= {seq(add(P[i],i=m..m+9),m=1..nops(P)-9)}: S10:= {seq(add(S[i],i=m..m+9),m=1..nops(S)-9)}: sort(convert(P10 intersect S10,list)); # Robert Israel, Mar 20 2017 -
Mathematica
With[{nn = 12600}, Intersection[Total /@ Partition[Prime@ Range@ PrimePi@ nn, 10, 1], Total /@ Partition[Select[Range@ nn, PrimeOmega@ # == 2 &], 10, 1]]] (* Michael De Vlieger, Mar 20 2017 *) -
PARI
list(lim)=if(lim<6504,return([])); my(v=List(),u=v,P=primes(9),x=(lim+10*log(lim))\1,t); forprime(p=2,x\2, forprime(q=2,min(x\p,p), listput(u,p*q))); u=Set(u); while(u[#u]+1+(t=sum(i=0,8,u[#u-i]))<=lim, for(n=x+1,lim-t, if(issemi(n), u=concat(u,n); next(2))); break); for(i=1,#u-9, u[i]+=sum(j=1,9,u[i+j])); t=vecsum(P); forprime(p=P[#P]+1,, t+=p; if(t>lim, break); if(setsearch(u,t), listput(v,t)); t-=P[1]; P=concat(P[2..9], p)); Vec(v) \\ Charles R Greathouse IV, Mar 20 2017