A270795
The prime/nonprime compound sequence BAB.
Original entry on oeis.org
4, 12, 21, 28, 34, 42, 52, 60, 65, 74, 84, 95, 98, 106, 119, 128, 133, 135, 141, 147, 170, 177, 180, 192, 195, 209, 214, 220, 231, 246, 250, 253, 284, 288, 290, 295, 301, 316, 323, 329, 336, 339, 351, 365, 382, 387, 390, 394, 417, 429, 432, 445, 462, 470, 474, 481, 490, 505, 516, 518, 532, 538, 543, 550, 559, 566
Offset: 1
Let A = primes
A000040, B = nonprimes
A018252. The 2-level compounds are AA =
A006450, AB =
A007821, BA =
A078782, BB =
A102615. The 3-level compounds AAA, AAB, ..., BBB are
A038580,
A049078,
A270792,
A102617,
A270794,
A270796,
A102216.
A175250
Nonprimes (A018252) with noncomposite (A008578) subscripts.
Original entry on oeis.org
1, 4, 6, 9, 12, 18, 21, 26, 28, 34, 42, 45, 52, 57, 60, 65, 74, 81, 84, 91, 95, 98, 106, 112, 119, 128, 133, 135, 141, 143
Offset: 1
a(5) = 12 because a(5) = b(q(5)) = b(7) = 12, q = noncomposite, b = nonprime.
A144574
Largest prime < nonprime(prime(n)).
Original entry on oeis.org
3, 5, 7, 11, 17, 19, 23, 23, 31, 41, 43, 47, 53, 59, 61, 73, 79, 83, 89, 89, 97, 103, 109, 113, 127, 131, 131, 139, 139, 139, 163, 167, 173, 179, 191, 193, 199, 199, 211, 211, 227, 229, 241, 241, 241, 251, 263, 283, 283, 283, 293, 293, 293, 313, 317, 317, 331
Offset: 1
a(1)=3 because nonprime(prime(1)) = nonprime(2) = 4 and the largest prime < 4 is 3;
a(2)=5 because nonprime(prime(2)) = nonprime(3) = 6 and the largest prime < 6 is 5.
-
A018252 := proc(n) if n = 1 then 1; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do: end if; end proc:
A078782 := proc(n) A018252(ithprime(n)) ; end proc:
A144574 := proc(n) prevprime(A078782(n)) ; end proc: seq(A144574(n),n=1..120) ;
# R. J. Mathar, May 01 2010
A161186
In the sequence of nonprime numbers, an element k's position is either prime or nonprime. If k's position is prime, f(k)= the k-th nonprime-positioned element, else f(k) is the k-th prime-positioned element. Iterated application of x-> f(x) gives disjoint sequences generated by the first elements, which form the current sequence.
Original entry on oeis.org
1, 6, 8, 9, 10, 12, 15, 18, 20, 21, 22, 25, 26, 27, 32, 33, 34, 35, 36, 38, 40, 44, 45, 48, 49, 50, 51, 52, 55, 57, 58, 62, 63, 64, 66, 69, 70, 72, 75, 76, 77, 78, 81, 82, 84, 85, 87, 88, 90, 91, 92, 93, 94, 98, 99, 100, 102, 104, 108, 110, 112, 114, 115, 116, 117, 120
Offset: 1
The nonprime numbers are: [1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20].
Those with prime positions are: [4, 6, 9, 12, 18].
Those with nonprime positions are: [1, 8, 10, 14, 15, 16, 20].
So we have {f(1)} = {1,4,14,60,...}, {f(6)} = {6,16,74,...}, {f(8)} ={8,28,56,...}; so the current sequence are the first elements, {1,6,8,...etc}.
-
lista(nn) = {my(va = select(x->(! isprime(x)), [1..nn])); my(vap = vector(primepi(#va), k, va[prime(k)])); my(vanp = Vec(setminus(va, vap))); my(vused = vector(#va), ok=1, last=0, list=List(), new, ok2); while(ok, last++; while ((last <= #vused) && vused[last], last++); if (last > #vused, break); new = va[last]; listput(list, new); ok2 = 1; my(list1 = List()); listput(list1, new); while(ok2, pos = setsearch(va, new); if (!pos, ok2=0, vused[pos] = 1; if (isprime(pos), if (new <= #vanp, new = vanp[new], ok2=0), if (new <= #vap, new = vap[new], ok2=0);); listput(list1, new);););); Vec(list);} \\ Michel Marcus, Aug 18 2022
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