A064149 - OEIS

%I #22 Oct 16 2024 09:23:49

%S 7,11,13,18,22,49,54,58,69,70,75,85,91,104,111,116,122,123,127,132,

%T 173,182,206,210,225,226,236,244,253,256,260,269,271,275,284,299,300,

%U 309,321,328,351,364,367,375,388,390,391,395,406,411,413,420,421,422,435

%N Indices of zeros of third differences of primes: Numbers k such that A036264(k) = 0.

%C Original definition: "Numbers k such that A036263(k) = A036263(k+1), using signed version of A036263."

%H Harry J. Smith, <a href="/A064149/b064149.txt">Table of n, a(n) for n = 1..1000</a>

%p q:= n-> is(add(ithprime(n+i)*binomial(3,i)*(-1)^i, i=0..3)=0):

%p select(q, [$1..500])[];  # _Alois P. Heinz_, Oct 15 2024

%o (PARI) { n=0; for (m=1, 10^9, if (prime(m) + 3*prime(m + 2) == 3*prime(m + 1) + prime(m + 3), write("b064149.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 09 2009

%o (PARI) select( {is_A064149(n)=!A064149(n)}, [1..444]) \\ _M. F. Hasler_, Oct 15 2024

%o (PARI) my(D(v)=v[^1]-v[^-1]); select(t->!t, D(D(D(primes(444)))), 1) \\ _M. F. Hasler_, Oct 15 2024

%Y Cf. A036263 (2nd differences of primes), A036264 (3rd differences of primes).

%K easy,nonn,changed

%O 1,1

%A _Jason Earls_, Sep 11 2001

%E Definition edited by _M. F. Hasler_, Oct 15 2024