A277123 Numbers k such that 1 + Sum_{j=1..k} prime(j)^2 is prime.
1, 11, 19, 29, 37, 73, 97, 155, 163, 175, 191, 257, 295, 313, 325, 341, 365, 389, 391, 409, 415, 461, 491, 497, 515, 599, 697, 715, 757, 761, 767, 775, 785, 793, 857, 875, 895, 899, 905, 919, 1099, 1109, 1117, 1139, 1151, 1163, 1225, 1271, 1279, 1295, 1309
Offset: 1
Keywords
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Position[Accumulate[Prime[Range[2000]]^2]+1,?PrimeQ]//Flatten (* _Harvey P. Dale, Sep 07 2019 *)
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PARI
lista(nn) = for(n=1, nn, if(isprime(1+sum(i=1, n, prime(i)^2)), print1(n, ", "))); \\ Altug Alkan, Oct 01 2016
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Python
import sympy sum = p = 1 for n in range(1,3001): while not sympy.isprime(p): p+=1 # find the n'th prime sum += p*p p+=1 if sympy.isprime(sum): print(n, end=', ')