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A303645 a(n) is the smallest number not yet seen such that sopfr(a(n)) is the least possible integer. 1
1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 12, 15, 16, 18, 14, 20, 24, 27, 21, 25, 30, 32, 36, 11, 28, 40, 45, 48, 54, 35, 42, 50, 60, 64, 72, 81, 13, 22, 56, 63, 75, 80, 90, 96, 108, 33, 49, 70, 84, 100, 120, 128, 135, 144, 162, 26, 44, 105, 112, 125, 126, 150, 160, 180, 192, 216, 243, 39, 55, 66, 98, 140, 168, 189 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is a permutation of the positive integers, listing in increasing order elements of the finite sets S(k) = {x: sopfr(x)=k}, k >= 0, where sopfr(x) = 0 iff x = 1. When a(n) = A056240(k) for some k >= 2, then sopfr(a(n)) = k and a(n) is the first of A000607(k) terms, all of which have sopfr = k. (A000607(k) is the number of partitions of k into prime parts.) Consequently the sequence follows a sawtooth profile, rising from a(n) = A056240(k) to A000792(k), the greatest number with sopfr = k, then starting over with A056240(k+1) for the next larger value of sopfr. [Edited by M. F. Hasler, Jan 19 2019]

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10077 (The b-file was updated Dec 14 2018 and is correct. - N. J. A. Sloane, Jan 19 2019)

FORMULA

If a(n) = A056240(k) for some k then a(n+A000607(k)-1) = A000792(k).

EXAMPLE

S(0) = {1}, S(1) = {}, S(2) = {2}, S(3) = {3}, S(4) = {4}, S(5) = {5, 6},

   S(6) = {8, 9}, S(7) = {7, 10, 12}, etc. Therefore the sequence begins:

   1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 12, .... [Edited by M. F. Hasler, Jan 19 2019]

PROG

(PARI) lista(nn) = {nmax = A000792(nn); v = vector(nmax, k, A001414(k)); for (n=1, nn, vn = select(x->x==n, v, 1); for (k = 1, #vn, print1(vn[k], ", ")))} \\ Michel Marcus, May 01 2018

(PARI) A303645_vec(N, k=6, L=9)={vector(N, i, if(i<7, N=i, until(A001414(N+=1)==k, ); N<L, N, k++; L=3^((k-2)\3)*(2+(k-2)%3); N+0*N=A056240(k)-1))} \\ To compute terms up to a given value of k=sopfr(n) and/or for large N >> 1000, it is more efficient to use code similar to lista() above, with "for(k...)" replaced by "a=concat(a, vn)". - M. F. Hasler, Jan 19 2019

CROSSREFS

Cf. A056240, A000607, A000792, A001414 (sopfr), A064364.

Sequence in context: A265552 A303936 A064364 * A269855 A209274 A303595

Adjacent sequences:  A303642 A303643 A303644 * A303646 A303647 A303648

KEYWORD

nonn

AUTHOR

David James Sycamore, Apr 27 2018

EXTENSIONS

Prepended 1. - N. J. A. Sloane, Dec 14 2018

Edited and b-file double-checked by M. F. Hasler, Jan 19 2019

STATUS

approved

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Last modified April 24 16:26 EDT 2019. Contains 322430 sequences. (Running on oeis4.)