A293894 Numbers n such that A083722(n) > 1 and A083722(n) occurs earlier in A083722.

27, 125, 147, 539, 2197, 2992, 3159, 3249, 3757, 4199, 4851, 5733, 6517, 11774, 15717, 16807, 19652, 20475, 25289, 28899, 30625, 31213, 31465, 33275, 34122, 41327, 43384, 44616, 50255, 60858, 61250, 61750, 62271

Offset

1,1

Comments

Equally, numbers n such that A293892(n) > 1 and A293892(n) <= max(A293892(1) .. A293892(n-1)).

Starts like A137800 except that term 3159 is not included in A137800, and furthermore, the latter sequence is not monotonic.

Question: Are there such runs of composites that contain three or more numbers whose largest prime factor is the same prime? In other words, is the intersection of A293893 and A293894 empty or not?

Links

David A. Corneth, Table of n, a(n) for n = 1..101

Mathematica

Flatten@ Values@ Map[Rest, Rest@ PositionIndex@ Array[Times @@ Select[Prime@ Range[#1, #1 + #2], Function[p, p <= #3]] & @@ {PrimePi@ NextPrime[FactorInteger[#][[-1, 1]]], PrimePi@ #, #} &, 10^4]] (* Michael De Vlieger, Nov 03 2017 *)

Prog

(PARI) upto(n) = {my(l = List(), p = 3, res = List, c); forprime(q = 5, nextprime(n + 1), for(i = p + 1, q - 1, f = factor(i)[, 1]; listput(l, [f[#f], precprime(i), i])); p = q); listsort(l); i = 1; while(i < #l - 1, if(l[i][1] == l[i+1][1], if(l[i][2] == l[i+1][2], listput(res, l[i+1][3]))); i++); listsort(res); res} \\ David A. Corneth, Nov 03 2017

Crossrefs

Cf. A083722, A137800, A293892, A293893.

Sequence in context: A209505 A275430 A145555 * A137800 A125497 A179145

Adjacent sequences: A293891 A293892 A293893 * A293895 A293896 A293897

Keyword

nonn

Author

Antti Karttunen, Nov 02 2017

Status

approved