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
Examples
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.
Links
- Christian Efrain Maldonado Sifuentes, Table of n, a(n) for n = 1..297
Programs
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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 *) -
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
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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.
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