A340771 Numbers which are the sum of some number of consecutive prime squares.

4, 9, 13, 25, 34, 38, 49, 74, 83, 87, 121, 169, 170, 195, 204, 208, 289, 290, 339, 361, 364, 373, 377, 458, 529, 579, 628, 650, 653, 662, 666, 819, 841, 890, 940, 961, 989, 1014, 1023, 1027, 1179, 1348, 1369, 1370, 1469, 1518, 1543, 1552, 1556, 1681, 1731, 1802, 1849

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Cathal O'Sullivan, Jonathan P. Sorenson, and Aryn Stahl, An Algorithm to Find Sums of Consecutive Powers of Primes, arXiv:2204.10930 [math.NT], 2022-2023. See S2 p. 10.

Janyarak Tongsomporn, Saeree Wananiyakul, and Jörn Steuding, Sums of Consecutive Prime Squares, arXiv:2101.07558 [math.NT], 2021.

Janyarak Tongsomporn, Saeree Wananiyakul, and Jörn Steuding, Sums of Consecutive Prime Squares, #A9 INTEGERS 22 (2022).

Example

The initial terms are 2^2, 3^2, 2^2+3^2, 5^2, 3^2+5^2, ...

Maple

N:= 10000: # for terms <= N
PS:= [0, seq(ithprime(i)^2, i=1..numtheory:-pi(floor(sqrt(N))))]:
SPS:= ListTools:-PartialSums(PS):
sort(convert(select(`<=`, {seq(seq(SPS[t]-SPS[s], s=1..t-1), t=2..nops(SPS))}, N), list)); # Robert Israel, Jan 20 2021

Prog

(PARI) lista(nn) = {my(list = List(), ip = primepi(nn), vp = primes(ip)); for(i=1, ip, my(s=vp[i]^2); listput(list, s); for (j=i+1, ip, s += vp[j]^2; if (s >vp[ip]^2, break); listput(list, s); ); ); Vec(vecsort(list, , 8)); } \\ Michel Marcus, Jan 20 2021

Crossrefs

Cf. A001248, A034707.

Sequence in context: A257337 A056227 A048261 * A333848 A063606 A033287

Adjacent sequences: A340768 A340769 A340770 * A340772 A340773 A340774

Keyword

nonn

Author

Michel Marcus, Jan 20 2021

Status

approved