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A293894
Numbers n such that A083722(n) > 1 and A083722(n) occurs earlier in A083722.
4
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 02 2017
STATUS
approved