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

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

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).

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 *)

Prog

(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

Crossrefs

Cf. A000040, A001358, A127337, A283873.

Sequence in context: A028544 A237245 A049529 * A338951 A251447 A156416

Adjacent sequences: A284099 A284100 A284101 * A284103 A284104 A284105

Keyword

nonn

Author

Zak Seidov, Mar 20 2017

Status

approved