A179437 -id:A179437 - cp's OEIS frontend

A331417 Maximum sum of primes of the parts of an integer partition of n.

0, 2, 4, 6, 8, 11, 13, 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, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 0

Gus Wiseman, Jan 17 2020

nonn

For n > 4, a(n) = prime(n).

Converges to A000040.
Row lengths of A331416.
The corresponding minimum is A007494.
Partitions whose sum of primes is divisible by their sum are A331379.
Cf. A000607, A001414, A014689, A056239, A179437, A330950, A330953, A330954, A331381, A331383, A331385, A331387, A331415, A331418.

Table[Max@@Table[Total[Prime/@y],{y,IntegerPartitions[n]}],{n,0,10}]

a(n) = A331418(n) + n - 1.

A144419 Primes of the form prime(k) - 2*k (terms can be repeated).

Original entry on oeis.org

3, 3, 5, 13, 17, 29, 31, 31, 37, 41, 47, 53, 67, 71, 71, 79, 79, 83, 89, 97, 97, 107, 107, 127, 131, 151, 181, 197, 211, 229, 241, 257, 257, 269, 271, 281, 283, 283, 311, 353, 373, 389, 401, 409, 409, 419, 419, 431, 449, 463, 479, 491, 499, 547, 563, 577, 577

Offset: 1

Juri-Stepan Gerasimov, Oct 07 2008

nonn

			For k=7,  prime(7)  - 2*7  = 17 - 14 =  3 = a(1).
For k=8,  prime(8)  - 2*8  =  9 - 16 =  3 = a(2).
For k=9,  prime(9)  - 2*9  = 23 - 18 =  5 = a(3).
For k=12, prime(12) - 2*12 = 37 - 24 = 13 = a(4).
For k=15, prime(15) - 2*15 = 47 - 30 = 17 = a(5).
For k=19, prime(19) - 2*19 = 67 - 38 = 29 = a(6).
For k=20, prime(20) - 2*20 = 71 - 40 = 31 = a(7).

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

Cf. A000040, A179437.

select(isprime, [seq(ithprime(k)-2*k,k=1..1000)]); # Robert Israel, Nov 24 2024

A 181 replaced with 281 by R. J. Mathar, Apr 14 2010

A173072 n-th prime minus n-th even number.

Original entry on oeis.org

2, 1, 1, 1, 3, 3, 5, 5, 7, 11, 11, 15, 17, 17, 19, 23, 27, 27, 31, 33, 33, 37, 39, 43, 49, 51, 51, 53, 53, 55, 67, 69, 73, 73, 81, 81, 85, 89, 91, 95, 99, 99, 107, 107, 109, 109, 119, 129, 131, 131, 133, 137, 137, 145, 149, 153, 157, 157, 161, 163, 163, 171, 183, 185

Offset: 1

Juri-Stepan Gerasimov, Feb 09 2010

See A179437 for another version.

Table[Prime[n]-2(n-1),{n,70}] (* Harvey P. Dale, Jul 04 2016 *)

a(n)=A000040(n) - 2n + 2.

Edited by Charles R Greathouse IV, Mar 24 2010

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A331417 Maximum sum of primes of the parts of an integer partition of n.

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A144419 Primes of the form prime(k) - 2*k (terms can be repeated).

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A173072 n-th prime minus n-th even number.

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