cp's OEIS Frontend

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.

A035141 Composite numbers k such that digits in k and in juxtaposition of prime factors of k are the same (apart from multiplicity).

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%I A035141 #21 Jul 30 2021 00:57:24
%S A035141 132,312,735,1255,1377,1775,1972,3792,4371,4773,5192,6769,7112,7236,
%T A035141 7371,7539,9321,11009,11099,11132,11163,11232,11255,11375,11913,12176,
%U A035141 12326,12595,12955,13092,13175,13312,13377,13491,13755,14842,15033
%N A035141 Composite numbers k such that digits in k and in juxtaposition of prime factors of k are the same (apart from multiplicity).
%H A035141 Charles R Greathouse IV, <a href="/A035141/b035141.txt">Table of n, a(n) for n = 1..10000</a>
%F A035141 a(n) ~ n. Proof: the density of numbers without a given decimal digit in their prime factors is 0, which can be seen by looking at the first (or second, in the case of 0) digit and removing all primes with that digit. Taken with the 0 density of numbers missing any decimal digit the result is obtained. - _Charles R Greathouse IV_, May 02 2013
%e A035141 1972 = {1,2,7,9} -> 2 * 2 * 17 * 29, so 1972 is a term.
%t A035141 Fac[n_]:=Sort[DeleteDuplicates[Flatten[IntegerDigits[Take[FactorInteger[n], All,1]]]]];Fn[n_]:=Sort[DeleteDuplicates[IntegerDigits[n]]];t={};Do[If[! PrimeQ[n]&&Fac[n]===Fn[n],AppendTo[t, n]],{n,2,15100}];t (* _Jayanta Basu_, May 02 2013 *)
%o A035141 (PARI) is(n)=if(isprime(n)||n<9,return(0));my(f=factor(n)[,1],v=[]);for(i=1,#f,v=concat(v,digits(f[i])));vecsort(digits(n),,8)==vecsort(v,,8) \\ _Charles R Greathouse IV_, May 02 2013
%Y A035141 Cf. A035139, A035140.
%K A035141 nonn,base
%O A035141 1,1
%A A035141 _Patrick De Geest_, Nov 15 1998
%E A035141 Definition corrected by _Charles R Greathouse IV_, May 02 2013