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A380564 Triangle read by rows q(b1,b2) with 1 with q(b1,b2) being the least integer k equal to or greater than b1 such that all the digits of k read in base b2 are the beginning digits of k read in base b1; or 0 iff b2 is perfect power, m^k (A001597), and b1 is m^j, 0

%I A380564 #39 Feb 05 2025 21:58:51
%S A380564 9,0,265,5,117032,2123333591,7,44,291720,10757067,57,449,16879,18042,
%T A380564 19032324921,0,332930,0,2180306,174631931663663360,51981761666123,9,0,
%U A380564 93,839,407917265,50732175,197761284636128964,10,10,133302001,124343,155133423353
%N A380564 Triangle read by rows q(b1,b2) with 1<b1<b2 with q(b1,b2) being the least integer k equal to or greater than b1 such that all the digits of k read in base b2 are the beginning digits of k read in base b1; or 0 iff b2 is perfect power, m^k (A001597), and b1 is m^j, 0<j<k.
%C A380564 a(703) has over 1000 digits, and so it is not included in the b-file.
%H A380564 Dominic McCarty, <a href="/A380564/b380564.txt">Table of n, a(n) for n = 1..702</a> (Rows 1..37).
%H A380564 Dominic McCarty, <a href="/A380564/a380564.txt">Python program</a>
%H A380564 Dominic McCarty, <a href="/A380564/a380564_1.txt">Illustrations of first 1830 terms</a>
%e A380564 a(1) = floor(A380599);
%e A380564 a(3) = q(3,4) = 265_10 = 10021_4 = 100211_3;
%e A380564 a(5) = q(4,5) = 117032_10 = 12221112_5 = 12221112112_3;
%e A380564 a(29) = floor(A379651); etc.
%e A380564 Lower triangle of an array:
%e A380564    \b1  2       3           4         5                   6               7
%e A380564   b2\
%e A380564    3|   9;
%e A380564    4|   0,    265;
%e A380564    5|   5, 117032, 2123333591;
%e A380564    6|   7,     44,     291720, 10757067;
%e A380564    7|  57,    449,      16879,    18042,        19032324921;
%e A380564    8|   0, 332930,          0,  2180306, 174631931663663360, 51981761666123;
%e A380564        ...
%Y A380564 Cf. A181929, A379651, A380599.
%K A380564 base,nonn,tabl
%O A380564 1,1
%A A380564 _Dominic McCarty_ and _Robert G. Wilson v_, Feb 03 2025