The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A331634 a(n) is the greatest possible least part of any prime partition of n. 9
 2, 3, 2, 5, 3, 7, 3, 3, 5, 11, 5, 13, 7, 5, 5, 17, 7, 19, 7, 7, 11, 23, 11, 7, 13, 7, 11, 29, 13, 31, 13, 11, 17, 11, 17, 37, 19, 13, 17, 41, 19, 43, 13, 13, 23, 47, 19, 13, 19, 17, 23, 53, 23, 17, 19, 19, 29, 59, 29, 61, 31, 17, 23, 19, 29, 67, 31, 23, 29, 71 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 2..12500 FORMULA For prime p>2, a(p) = a(2*p) = a(3*p) = p. EXAMPLE a(12) = 5, because 5 is the largest of all minimal primes in partitions of 12 into prime parts: [2,2,2,2,2,2], [2,2,2,3,3], [3,3,3,3], [2,2,3,5], [2,5,5], [2,3,7], [5,7]. MAPLE b:= proc(n, p, t) option remember; `if`(n=0, 1, `if`(p>n, 0, (q-> add(b(n-p*j, q, 1), j=1..n/p)*t^p+b(n, q, t))(nextprime(p)))) end: a:= n-> degree(b(n, 2, x)): seq(a(n), n=2..100); # Alois P. Heinz, Mar 13 2020 MATHEMATICA Array[If[PrimeQ@ #, #, Max@ IntegerPartitions[#, #/FactorInteger[#][[1, 1]], Prime@ Range@ PrimePi[# - 2]][[All, -1]] ] &, 60, 2] (* Michael De Vlieger, Jan 26 2020 *) (* Second program: *) b[n_, p_, t_] := b[n, p, t] = If[n == 0, 1, If[p > n, 0, Function[q, Sum[ b[n - p*j, q, 1], {j, 1, n/p}]*t^p + b[n, q, t]][NextPrime[p]]]]; a[n_] := Exponent[b[n, 2, x], x]; a /@ Range[2, 100] (* Jean-François Alcover, Jun 04 2021, after Alois P. Heinz *) CROSSREFS Cf. A000040, A000607, A001414, A100484, A001748. Sequence in context: A284695 A081812 A356427 * A370833 A341676 A139421 Adjacent sequences: A331631 A331632 A331633 * A331635 A331636 A331637 KEYWORD nonn AUTHOR David James Sycamore, Jan 23 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 3 21:27 EDT 2024. Contains 374905 sequences. (Running on oeis4.)