A126955 -id:A126955 - cp's OEIS frontend

A376848 Numbers k such that phi(k + phi(k)) = phi(k) + phi(phi(k)), where phi = A000010.

2, 5, 9, 10, 14, 18, 20, 27, 28, 36, 38, 40, 46, 54, 56, 72, 76, 78, 80, 81, 92, 108, 112, 144, 152, 156, 160, 162, 184, 216, 224, 234, 243, 258, 288, 294, 304, 312, 320, 324, 368, 432, 438, 448, 468, 486, 516, 526, 570, 576, 588, 608, 609, 624, 640, 648, 702, 718, 729, 736, 754, 774, 864, 876

Offset: 1

Robert Israel, Oct 06 2024

nonn

If k is in A126955, then 8*k + 6 is a term.

			a(4) = 10 is a term because phi(10) = 4, phi(4) = 2, and phi(10 + 4) = phi(14) = 6 = 4 + 2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000010, A126955, A376830, A376831, A376843, A376844, A376849, A376851.

filter:= proc(k) uses numtheory; local s;
 s:= phi(k);
 phi(k+s) = s + phi(s)
end proc:
select(filter, [$1..1000]);

Select[Range[880], EulerPhi[ #+EulerPhi[#]]==EulerPhi[#]+EulerPhi[EulerPhi[#]] &] (* Stefano Spezia, Oct 07 2024 *)

A126956 Numbers n such that 3n+2, 4n+3 and 5n+4 are primes.

Original entry on oeis.org

5, 17, 77, 89, 119, 185, 257, 287, 395, 665, 755, 797, 929, 1175, 1259, 1337, 1379, 1445, 1469, 1769, 2057, 2105, 3125, 3419, 3437, 3629, 3815, 3989, 4079, 4157, 4175, 4217, 4367, 4445, 4847, 5045, 5375, 6089, 6137, 6167, 6359, 6419, 6485, 6725, 6887

Offset: 1

J. M. Bergot, Mar 19 2007

nonn

			Take n = 185. Then 3*185 + 2 = 557, 4*185 + 3 = 743 and 5*185 + 4 = 929 are primes.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Intersection of A024893, A095278, A024897. Cf. A126955.

Select[Range[7000], PrimeQ[3# + 2] && PrimeQ[4# + 3] && PrimeQ[5# + 4] &] (* Ray Chandler, Mar 20 2007 *)
Select[Range[7000],AllTrue[{3#+2,4#+3,5#+4},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 06 2019 *)

Corrected and extended by Ray Chandler, Stuart Clary, Robert G. Wilson v and Zak Seidov, Mar 20 2007

cp's OEIS Frontend

A376848 Numbers k such that phi(k + phi(k)) = phi(k) + phi(phi(k)), where phi = A000010.

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