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A331272 Irregular triangle in which row n lists numbers m such that A330073(m,n) = 1.

%I A331272 #36 Aug 06 2024 11:13:21
%S A331272 1,5,25,4,125,20,625,3,100,104,3125,15,16,500,520,15625,2,75,80,83,86,
%T A331272 2500,2600,2604,78125,10,12,13,375,400,415,416,430,433,12500,13000,
%U A331272 13020,390625,50,60,62,65,66,69,71,1875,2000,2075,2080,2083,2150,2165,2166,62500,65000,65100,65104,1953125
%N A331272 Irregular triangle in which row n lists numbers m such that A330073(m,n) = 1.
%C A331272 The last number in row n is 5^n (A000351(n)).
%C A331272 For numbers m and n such that m is in row n, 5*m is in row n + 1 and if m > 10 and m == 10, 15, 20, or 25 (mod 30), then floor(m/6) is in row n + 1.
%C A331272 The conjecture in A330073 claims that every positive integer appears in this triangle.
%H A331272 T. Ahmed and H. Snevily, <a href="https://citeseerx.ist.psu.edu/pdf/2207919fcc0e2e4336faf345389c5dcd2daea50e">Are There an Infinite Number of Collatz Integers?</a>, 2013.
%H A331272 M. Bruschi, <a href="https://arxiv.org/abs/0810.5169">A generalization of the Collatz problem and conjecture</a>, arXiv:0810.5169 [math.NT], 2008.
%H A331272 W. Carnielli, <a href="https://www.emis.de/journals/AMEN/2015/AMEN(150711).pdf">Some Natural Generalizations Of The Collatz Problem</a>, Applied Mathematics E-Notes, 15 (2015), 197-206.
%F A331272 If N is the list of numbers in row n, then the list of numbers in row n + 1 is the union of each number in N multiplied by 5 and numbers floor(x/6) where x is in N, congruent to 0 (mod 5), not congruent to 0 or 5 (mod 30), and floor(x/6) > 1.
%e A331272 The irregular triangle starts:
%e A331272 0:   1
%e A331272 1:   5
%e A331272 2:  25
%e A331272 3:   4  125
%e A331272 4:  20  625
%e A331272 5:   3  100  104 3125
%e A331272 6:  15   16  500  520 15625
%e A331272 7:   2   75   80   83    86  2500  2600  2604 78125
%e A331272 8:  10   12   13  375   400   415   416   430   433 12500 13000 13020 390625
%o A331272 (PARI) A331272(lim)=my(N=[1], b=-1, RC=5*[2..5]); while(b<lim, b++;print(N);N=vecsort(matconcat(apply(X->if(setsearch(RC,X%30)&&(X>RC[1]),[floor(X/6),5*X],X*5),N))[1,]))
%Y A331272 Cf. A000351 (5^n), A127824, A330073.
%K A331272 nonn,easy,tabf,look
%O A331272 0,2
%A A331272 _Davis Smith_, Jan 13 2020