A064149 Indices of zeros of third differences of primes: Numbers k such that A036264(k) = 0.

7, 11, 13, 18, 22, 49, 54, 58, 69, 70, 75, 85, 91, 104, 111, 116, 122, 123, 127, 132, 173, 182, 206, 210, 225, 226, 236, 244, 253, 256, 260, 269, 271, 275, 284, 299, 300, 309, 321, 328, 351, 364, 367, 375, 388, 390, 391, 395, 406, 411, 413, 420, 421, 422, 435

Offset

1,1

Comments

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

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Maple

q:= n-> is(add(ithprime(n+i)*binomial(3, i)*(-1)^i, i=0..3)=0):
select(q, [$1..500])[];  # Alois P. Heinz, Oct 15 2024

Mathematica

Position[Differences[Prime[Range[1000]], 3], 0] // Flatten (* Jean-François Alcover, Nov 20 2024 *)

Prog

(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
(PARI) select( {is_A064149(n)=!A064149(n)}, [1..444]) \\ M. F. Hasler, Oct 15 2024
(PARI) my(D(v)=v[^1]-v[^-1]); select(t->!t, D(D(D(primes(444)))), 1) \\ M. F. Hasler, Oct 15 2024

Crossrefs

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

Sequence in context: A153321 A060772 A257125 * A046289 A092246 A084468

Adjacent sequences: A064146 A064147 A064148 * A064150 A064151 A064152

Keyword

easy,nonn,changed

Author

Jason Earls, Sep 11 2001

Extensions

Definition edited by M. F. Hasler, Oct 15 2024

Status

approved