This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A138510 #23 Sep 23 2018 22:30:26 %S A138510 1,2,1,6,8,3,3,12,1,14,12,18,2,20,14,24,1,18,4,20,30,32,4,24,38,4,42, %T A138510 5,44,30,4,32,48,5,54,38,5,60,5,1,62,42,44,5,68,48,72,2,30,74,32,80, %U A138510 54,5,84,1,60,90,62,38,3,98,68,102,6,42,104,3,72,108,44,6,110,74,3,114,48,80 %N A138510 Smallest number b such that in base b the prime factors of the n-th semiprime (A001358) have equal lengths. %C A138510 a(n) = 1 iff A001358(n) is the square of a prime (A001248); %C A138510 a(A174956(A138511(n))) = A084127(A174956(A138511(n))) + 1. %C A138510 Equally, 1 if A001358(n) = p^2, otherwise, if A001358(n) = p*q (p, q primes, p < q), then a(n) = A252375(n) = the least r such that r^k <= p < q < r^(k+1), for some k >= 0. - _Antti Karttunen_, Dec 16 2014 %C A138510 a(A174956(A085721(n))) <= 2. - _Reinhard Zumkeller_, Dec 19 2014 %H A138510 Reinhard Zumkeller, <a href="/A138510/b138510.txt">Table of n, a(n) for n = 1..10000</a> %F A138510 a(n) = A251725(A001358(n)). - _Antti Karttunen_, Dec 16 2014 %e A138510 For n=31, the n-th semiprime is A001358(31) = 91 = 7*13; %e A138510 7 = 111_2 = 21_3 = 13_4 %e A138510 and 13 = 1101_2 = 111_3 = 31_4, so a(31) = 4. [corrected by _Jon E. Schoenfield_, Sep 23 2018] %e A138510 . %e A138510 Illustration of initial terms, n <= 25: %e A138510 . n | A001358(n) = p * q | b = a(n) | p and q in base b %e A138510 . ----+---------------------+-----------+------------------- %e A138510 . 1 | 4 2 2 | 1 | [1] [1] %e A138510 . 2 | 6 2 3 | 2 | [1,0] [1,1] %e A138510 . 3 | 9 3 3 | 1 | [1,1,1] [1,1,1] %e A138510 . 4 | ** 10 2 5 | 6 | [2] [5] %e A138510 . 5 | ** 14 2 7 | 8 | [2] [7] %e A138510 . 6 | 15 3 5 | 3 | [1,0] [1,2] %e A138510 . 7 | 21 3 7 | 3 | [1,0] [2,1] %e A138510 . 8 | ** 22 2 11 | 12 | [2] [11] %e A138510 . 9 | 25 5 5 | 1 | [1]^5 [1]^5 %e A138510 . 10 | ** 26 2 13 | 14 | [2] [13] %e A138510 . 11 | ** 33 3 11 | 12 | [3] [11] %e A138510 . 12 | ** 34 2 17 | 18 | [2] [17] %e A138510 . 13 | 35 5 7 | 2 | [1,0,1] [1,1,1] %e A138510 . 14 | ** 38 2 19 | 20 | [2] [19] %e A138510 . 15 | ** 39 3 13 | 14 | [3] [13] %e A138510 . 16 | ** 46 2 23 | 24 | [2] [23] %e A138510 . 17 | 49 7 7 | 1 | [1]^7 [1]^7 %e A138510 . 18 | ** 51 3 17 | 18 | [3] [17] %e A138510 . 19 | 55 5 11 | 4 | [1,1] [2,3] %e A138510 . 20 | ** 57 3 19 | 20 | [3] [19] %e A138510 . 21 | ** 58 2 29 | 30 | [2] [29] %e A138510 . 22 | ** 62 2 31 | 32 | [2] [31] %e A138510 . 23 | 65 5 13 | 4 | [1,1] [3,1] %e A138510 . 24 | ** 69 3 23 | 24 | [3] [23] %e A138510 . 25 | ** 74 2 37 | 38 | [2] [37] %e A138510 where p = A084126(n) and q = A084127(n), %e A138510 semiprimes marked with ** indicate terms of A138511, i.e. b = q + 1. %o A138510 (Haskell) %o A138510 import Data.List (genericIndex, unfoldr); import Data.Tuple (swap) %o A138510 import Data.Maybe (mapMaybe) %o A138510 a138510 n = genericIndex a138510_list (n - 1) %o A138510 a138510_list = mapMaybe f [1..] where %o A138510 f x | a010051' q == 0 = Nothing %o A138510 | q == p = Just 1 %o A138510 | otherwise = Just $ %o A138510 head [b | b <- [2..], length (d b p) == length (d b q)] %o A138510 where q = div x p; p = a020639 x %o A138510 d b = unfoldr (\z -> if z == 0 then Nothing else Just $ swap $ divMod z b) %o A138510 -- _Reinhard Zumkeller_, Dec 16 2014 %o A138510 (Scheme) (define (A138510 n) (A251725 (A001358 n))) ;; _Antti Karttunen_, Dec 16 2014 %Y A138510 Cf. A078972, A085721. %Y A138510 Cf. A138511, A251728, A252375, A084127, A020639, A162319, A174956, A001358. %K A138510 nonn,base %O A138510 1,2 %A A138510 _Reinhard Zumkeller_, Mar 21 2008 %E A138510 Wrong comment corrected by _Reinhard Zumkeller_, Dec 16 2014