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 A340771 Numbers which are the sum of some number of consecutive prime squares. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..53. 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. 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

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Last modified June 3 18:44 EDT 2023. Contains 363116 sequences. (Running on oeis4.)