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A376916
Primes that are the sum of some number of consecutive prime squares.
1
13, 83, 373, 653, 1543, 2393, 3271, 4519, 4723, 5381, 6701, 7591, 8069, 8219, 9439, 10453, 11719, 19541, 20269, 20477, 23599, 24821, 24953, 32939, 35323, 38219, 39631, 41539, 45319, 51031, 53549, 55721, 56179, 56383, 56599, 56909, 65419, 69389, 73331, 74441, 75997, 81299, 87589, 89459, 90199, 93581, 96661, 97847, 98017, 107741, 108827, 109849
OFFSET
1,1
COMMENTS
Primes in A340771.
LINKS
EXAMPLE
a(3) = 373 is a term because 373 is prime and 373 = 3^2 + 5^2 + 7^2 + 11^2 + 13^2 where 3, 5, 6, 11 and 13 are consecutive primes.
MAPLE
N:= 2*10^5: # for terms <= N
PS:= [0, seq(ithprime(i)^2, i=1..numtheory:-pi(floor(sqrt(N))))]:
SPS:= ListTools:-PartialSums(PS):
sort(convert(select(t -> t <= N and isprime(t), {seq(seq(SPS[t]-SPS[s], s=1..t-2), t=2..nops(SPS))}), list);
CROSSREFS
Cf. A340771.
Sequence in context: A101102 A213572 A142085 * A163688 A274398 A301953
KEYWORD
nonn
AUTHOR
Robert Israel, Oct 09 2024
STATUS
approved