A320228 Distribute the primes into groups in ascending order, with the n-th group having prime(n) elements. Then a(n) is the sum of the numbers in the n-th group times the number of elements in the group.

10, 69, 505, 2177, 10241, 24635, 65875, 120631, 244789, 531715, 802063, 1464941, 2279887, 3065943, 4444273, 6747695, 9882205, 12447843, 17304961, 22371177, 26991677, 35679165, 44240245, 56968633, 75590451, 91181689, 104420885, 124020811, 141249939, 164746655

Offset

1,1

Comments

On every step we sum prime(n) elements from the prime list and multiply the result by the number of elements of the sum.

Links

Christian Efrain Maldonado Sifuentes, Table of n, a(n) for n = 1..297

Formula

a(n) = A000040(n)*A034958(n). - Michel Marcus, Oct 08 2018

Example

a(1) =   10 because "sum of next 2 primes times 2" is (2+3)*2;
a(2) =   69 because "sum of next 3 primes times 3" is (5+7+11)*3;
a(3) =  505 because "sum of next 5 primes times 5" is (13+17+19+23+29)*5;
a(4) = 2177 because "sum of next 7 primes times 7" is (31+37+41+43+47+53+59)*7.

Mathematica

With[{s = Prime@ Range[10^4]}, Rest@Nest[Append[#, {MapAt[Length[#] Total[#] &, TakeDrop[#[[-1, 1, 2]], Prime@ #[[-1, -1]]], 1], #[[-1, -1]] + 1}] &, {{{{}, s}, 1}}, 30]][[All, 1, 1]] (* Michael De Vlieger, Oct 15 2018 *)

Prog

(PHP)
for ($n=1; $i<$maxTestedNumber; $n=$i+1){
    if(isPrime($n)){
        while ($amountOfPrimes < $n){
        if (isPrime($currNum)){
            $sumPrimes = $sumPrimes + $currNum;
            $amountOfPrimes++;
            }
        $currentNumber=$currentNumber+1;
        }
        $sumPrimesTimesN = $n*$sumPrimes;
        echo "$sumPrimesTimesN, ";
        $sumPrimes=0;      //Reset for next cycle
        $amountOfPrimes=0; //Reset for next cycle
    }
//isPrime can be any function that returns TRUE if the tested number is prime and FALSE if the tested number is not prime.
(PARI) s(n) = sum(k=1, n, prime(k)); \\ A007504
f(n) = s(s(n)) - s(s(n-1)); \\ A034958
a(n) = prime(n)*f(n); \\ Michel Marcus, Oct 12 2018

Crossrefs

Cf. A000040, A007504, A034958.

Sequence in context: A038806 A016273 A128737 * A130548 A160662 A090084

Adjacent sequences: A320225 A320226 A320227 * A320229 A320230 A320231

Keyword

nonn,easy

Author

Christian Efrain Maldonado Sifuentes, Oct 07 2018

Status

approved