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Differences of A011757 ("Primes with square indices").
3

%I #16 May 01 2023 12:50:55

%S 5,16,30,44,54,76,84,108,122,120,166,182,184,234,192,260,264,294,304,

%T 342,378,342,408,426,414,468,488,474,516,576,588,576,604,590,696,694,

%U 728,694,756,828,774,776,870,862,852,1010,922,998,916,1020,1032,1110

%N Differences of A011757 ("Primes with square indices").

%C Does a(n) = k^2 have infinitely many solutions? E.g., 16 = 4^2; 576 = 24^2; ...

%H Harry J. Smith, <a href="/A063076/b063076.txt">Table of n, a(n) for n = 1..1000</a>

%t Differences[Prime[Range[60]^2]] (* _Harvey P. Dale_, May 01 2023 *)

%o (PARI) j=[]; for(n=1,150,j=concat(j, prime((n+1)^2)-prime(n^2))); j

%o (PARI) { default(primelimit, 2*10^7); for (n=1, 1000, write("b063076.txt", n, " ", prime((n+1)^2) - prime(n^2)) ) } \\ _Harry J. Smith_, Aug 17 2009

%Y Cf. A011757, A063082.

%K nonn

%O 1,1

%A _Santi Spadaro_, Aug 04 2001

%E More terms from _Jason Earls_, Aug 05 2001