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Primes For primes of the form (7+k!)/7 , see A139064.

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11, 15, 16, 25, 35, 59, 64, 68, 82, 121, 149, 238, 584, 912, 3349, 4111, 4324, 15314, 19944, 20658, 22740, 23364

a(23) > 25000. - Robert Price, Nov 20 2016

a(18)-a(22) from Robert Price, Nov 20 2016

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Numbers k for which (7 + k!)/7 is prime.

For primes Primes of the form (7 + k!)/7, see A139064.

Formulation: Such sequences can be generated by writing k in increasing order provided that A000142(k) = [|c|]*(A000040(m)-1) for some m where |.| is the absolute value function and [.] is either the ceiling function or floor function, where c is complex number. Abdul Gaffar Khan, Nov 29 2015

a(n) = k if A000142(k) = 7*(A000040(m)-1) for some m. - Abdul Gaffar Khan, Nov 29 2015

For example, in A139065, if [.] is ceiling function let c=-6.4+0.2i, if [.] is floor function let c=-7.4+0.2i in particular.For other examples of formulation, see A002981, A082672, A089085, A139058, A139063, ... etc. Abdul Gaffar Khan, Nov 29 2015

A139065[n_] := If[PrimeQ[(7 + (n!))*(1/7)] == True, n, 0];

Delete[DeleteDuplicates[Table[A139065[n], {n, 0, 64}]], 1] (* Abdul Gaffar Khan, Nov 29 2015 *)

A139065[n_] :=

If[PrimeQ[(Ceiling[

Abs[c]] + (FromDigits[IntegerDigits[n, 10]])!)*(1/

Ceiling[Abs[c]])] == True, n, 0];

Delete[DeleteDuplicates[Table[A139065[n], {n, 0, 64}]], 1]

(* replace complex number in place of c to get sequences of type A139065* *and Replace Ceiling with Floor for formluation of complex numbers*) (* Abdul Gaffar Khan, Dec 02 2015 *)

(MAGMA) [n: n in [7..300] | IsPrime((7 + Factorial(n)) div 7)]; // Vincenzo Librandi, Nov 30 2015

nonn,hard,more,changed

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From _Formulation: Such sequences can be generated by writing k in increasing order provided that A000142(k) = [|c|]*(A000040(m)-1) for some m where |.| is the absolute value function and [.] is either the ceiling function or floor function, where c is complex number. _Abdul Gaffar Khan_, Nov 29 2015: (Start)

Formulation:

(a) For Real Numbers:

Such sequences can be generated by writing k in increasing order provided that A000142(k) = |[j]|*(A000040(m)-1) for some m where |.| is modulus function, [.] is either the ceiling function or floor function, and |[j]| = q where j is real number lying in the set as follows: if [.] is ceiling function, then j lies in set {j|q-1<j<=q or -q<=j<q+1} and if [.] is floor function then j lies in set {j|q<=j<q+1 or -q<j<=q}. For example, in A139065, if [.] is ceiling function then j lies in set {j|6<j<=7 or -7<=j<8} and if [.] is floor function then j lies in set {j|7<=j<8 or -6<j<=7}.

(b) For Complex Numbers:

Such sequences can be generated by writing k in increasing order provided that A000142(k) = [|c|]*(A000040(m)-1) for some m where |.| is the absolute value function and [.] is either the ceiling function or floor function, where c is complex number. For example, in A139065, if [.] is ceiling function let c=-6.4+0.2i, if [.] is floor function let c=-7.4+0.2i in particular.

For other examples, see A002981, A082672, A089085, A139058, A139063, ... etc.

(End)

For example, in A139065, if [.] is ceiling function let c=-6.4+0.2i, if [.] is floor function let c=-7.4+0.2i in particular.For other examples of formulation, see A002981, A082672, A089085, A139058, A139063, ... etc. Abdul Gaffar Khan, Nov 29 2015

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