A163997 -id:A163997 - cp's OEIS frontend

A163998 Primes p having the same parity as the number of partitions of p.

2, 3, 5, 7, 13, 17, 23, 29, 37, 41, 43, 53, 61, 67, 71, 73, 83, 89, 107, 127, 139, 157, 173, 181, 193, 199, 211, 223, 229, 233, 239, 251, 257, 263, 269, 277, 281, 283, 293, 311, 313, 331, 349, 367, 373, 389, 401, 421, 433, 443, 457, 461, 463, 467, 479, 491, 499

Offset: 1

Omar E. Pol, Aug 09 2009

nonn

Except the first term, primes with an odd number of partitions.

Primes in A194798. - Omar E. Pol, Mar 17 2012

			7 is in the sequence because the number of partitions of 7 is equal to 15 and both 7 and 15 have the same parity.

Cf. A000040, A000041, A040051, A052002, A163997, A194798.

Select[Prime[Range[100]], Mod[PartitionsP[#] - #, 2] == 0 &] (* T. D. Noe, Jan 30 2012 *)

More terms from D. S. McNeil, May 10 2010

A163996 Primes with a composite number of partitions.

Original entry on oeis.org

7, 11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293

Offset: 1

Omar E. Pol, Aug 09 2009

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
Omar E. Pol, Illustration of the shell model of partitions (3D view)

Cf. A000040, A000041, A002808, A038601, A135010, A163997, A163998.

Select[Prime[Range[100]],!PrimeQ[PartitionsP[#]]&] (* Harvey P. Dale, Jun 22 2014 *)

A000040 \ A038601. [From R. J. Mathar, Sep 27 2009]

More terms from R. J. Mathar, Sep 27 2009

A193830 Even partition numbers of prime numbers.

Original entry on oeis.org

2, 56, 490, 6842, 124754, 831820, 13848650, 133230930, 214481126, 271248950, 541946240, 851376628, 5964539504, 11097645016, 37027355200, 45060624582, 142798995930, 207890420102, 625846753120, 1820701100652, 3068829878530, 37561133582570, 114540884553038

Offset: 1

Omar E. Pol, Aug 06 2011

nonn

			The even number 56 is in the sequence as the partition number of the prime number 11.

Even numbers in A058698.

Cf. A000040, A000041, A052001, A154796, A154798, A163997, A193831.

Select[PartitionsP[Prime[Range[200]]],EvenQ] (* Harvey P. Dale, Jun 20 2015 *)

cp's OEIS Frontend

A163998 Primes p having the same parity as the number of partitions of p.

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A163996 Primes with a composite number of partitions.

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A193830 Even partition numbers of prime numbers.

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