A069348 -id:A069348 - cp's OEIS frontend

A069351 Primes having no representation of the form n + A001222(n), complement of A069348.

2, 5, 7, 13, 19, 29, 43, 61, 83, 103, 107, 109, 137, 149, 197, 227, 263, 281, 283, 347, 349, 353, 389, 443, 457, 467, 479, 523, 541, 563, 569, 571, 587, 619, 643, 647, 653, 659, 677, 743, 761, 797, 811, 821, 827, 863, 883, 937

Offset: 1

Reinhard Zumkeller, Mar 18 2002

nonn

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

Cf. A069350.

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

A069349 Number of ways to represent primes as A069348(n)=k+A001222(k).

Original entry on oeis.org

1, 2, 1, 2, 1, 2, 1, 1, 3, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 2, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 3, 3, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2

Offset: 1

Reinhard Zumkeller, Mar 18 2002

nonn

			a(9)=3 as: A069348(9)=53=A064800(48)=A064800(50)=A064800(51)
53=2*2*2*2*3+5 and 53=2*5*5+3 and 51=3*17+2.

A069346 Primes of the form n - Omega(n), where Omega(n) is the number of prime factors of n, A001222(n).

Original entry on oeis.org

2, 5, 7, 13, 17, 19, 23, 31, 37, 41, 43, 47, 53, 67, 73, 83, 89, 103, 107, 109, 113, 127, 131, 139, 151, 157, 163, 167, 179, 181, 199, 211, 227, 233, 239, 241, 251, 257, 263, 281, 283, 293, 307, 311, 313, 317, 337, 347, 353, 359

Offset: 1

Reinhard Zumkeller, Mar 18 2002

nonn

The representation is ambiguous, see A069347.

			a(10) = 41 = A069345(44) = 44-3 (as 44 = 2*2*11).

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

Cf. A069348, A069356.

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

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

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

A173032 Primes having no representation of the form n -+ Omega(n), where Omega is A001222.

Original entry on oeis.org

29, 61, 137, 149, 197, 349, 457, 523, 569, 619, 659, 1091, 1153, 1303, 1483, 1549, 1723, 1861, 1873, 2339, 2347, 2377, 2593, 2753, 2851, 3121, 3169, 3257, 3323, 3391, 3469, 3539, 4051, 4177, 4373, 4423, 4483, 4547, 4691, 4799, 4877, 4933, 4943, 5101, 5237

Offset: 1

Juri-Stepan Gerasimov, Nov 21 2010

nonn

Intersection of A069350 and A069351.

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

Cf. A069346, A069348, A001222.

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

cp's OEIS Frontend

A069351 Primes having no representation of the form n + A001222(n), complement of A069348.

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A069349 Number of ways to represent primes as A069348(n)=k+A001222(k).

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A069346 Primes of the form n - Omega(n), where Omega(n) is the number of prime factors of n, A001222(n).

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

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A173032 Primes having no representation of the form n -+ Omega(n), where Omega is A001222.

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