A069357 -id:A069357 - cp's OEIS frontend

A069348 Primes of the form k + Omega(k), where Omega(k) is the number of prime factors of k, A001222(k).

3, 11, 17, 23, 31, 37, 41, 47, 53, 59, 67, 71, 73, 79, 89, 97, 101, 113, 127, 131, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 199, 211, 223, 229, 233, 239, 241, 251, 257, 269, 271, 277, 293, 307, 311, 313, 317, 331, 337

Offset: 1

Reinhard Zumkeller, Mar 18 2002

nonn

The representation is ambiguous, see A069349.

			a(10) = 59 = A064800(57) = 57 + 2 (as 57 = 3*19).

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A069346, A069357.

Select[Table[n + PrimeOmega[n], {n, 1, 400}], PrimeQ] // Union (* Jean-François Alcover, Jun 08 2013 *)

is(n)=for(k=1,log(n+.5)\log(2),if(bigomega(n-k)==k,return(isprime(n)))); 0 \\ Charles R Greathouse IV, Dec 10 2013

Corrected by T. D. Noe, Nov 01 2006

A069355 Numbers of form 2^i*3^j - (i+j) with i, j >= 0.

Original entry on oeis.org

1, 2, 4, 5, 7, 9, 12, 15, 20, 24, 27, 32, 43, 50, 58, 67, 77, 90, 103, 121, 138, 157, 185, 210, 238, 248, 281, 318, 376, 425, 480, 503, 568, 641, 723, 759, 856, 965, 1014, 1143, 1288, 1451, 1526, 1719, 1936, 2037, 2180, 2294, 2583, 2908, 3061, 3446, 3879, 4084

Offset: 1

Reinhard Zumkeller, Mar 18 2002

nonn

Distinct values of A003586(m)-A069352(m) or of A069345(A003586(m)). - Michel Marcus, Apr 09 2018

			1 is a term because 2^0*3^0 - (0+0) = 2^1*3^0 - (1+0) = 1.
2 is a term because 2^2*3^0 - (2+0) = 2^0*3^1 - (0+1) = 2.
4 is a term because 2^1*3^1 - (1+1) = 4.

Cf. A003586, A069345, A069352, A069353, A069356, A069357, A022328, A022329.

With[{nn=20},Take[Flatten[Table[2^i 3^j-i-j,{i,0,nn},{j,0,nn}]]//Union,60]] (* Harvey P. Dale, Aug 29 2022 *)

Duplicated term 2 and incorrect formula removed by Altug Alkan, Apr 09 2018

A069358 Primes of the form 2^i*3^j + (i+j) with i, j >= 0.

Original entry on oeis.org

3, 11, 37, 53, 113, 167, 199, 439, 521, 3083, 6569, 12301, 23339, 32783, 139981, 663569, 708601, 3981331, 7558289, 20155411, 38263769, 45349651, 75497497, 483729431, 1934917657, 2717909021, 6115295261, 12397455671, 14693280793

Offset: 1

Reinhard Zumkeller, Mar 18 2002

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300 [Corrected by Sean A. Irvine]

Cf. A069357, A005109, A069356, A069348.

Take[ Select[ Union[ Flatten[ Table[2^i*3^j + (i + j), {i, 0, 25}, {j, 0, 18}]]], PrimeQ[ # ] &], 30]

Edited and extended by Robert G. Wilson v, May 09 2003

cp's OEIS Frontend

A069348 Primes of the form k + Omega(k), where Omega(k) is the number of prime factors of k, A001222(k).

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A069355 Numbers of form 2^i*3^j - (i+j) with i, j >= 0.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A069358 Primes of the form 2^i*3^j + (i+j) with i, j >= 0.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions