cp's OEIS Frontend

A271630 Composite numbers n coprime to all number that can be obtained by changing just one digit of n.

%I A271630 #25 Apr 15 2016 09:58:17
%S A271630 121,143,169,187,209,221,247,253,289,299,319,323,341,343,361,377,391,
%T A271630 403,407,437,451,473,481,493,517,527,529,533,551,553,559,583,589,611,
%U A271630 629,649,667,671,689,697,703,713,731,737,767,779,781,793,799,803,817,841,851
%N A271630 Composite numbers n coprime to all number that can be obtained by changing just one digit of n.
%C A271630 Only numbers ending in 1, 3, 7 and 9.
%C A271630 Apart from the first 10 terms, A078972 is a subset of this sequence.
%C A271630 Subsequence of A038510. - _Altug Alkan_, Apr 15 2016
%C A271630 Least squareless numbers with increasing number of primes:
%C A271630 143 = 11 * 13;
%C A271630 2431 = 11 * 13 * 17;
%C A271630 45353 = 7 * 11 * 19 * 31;
%C A271630 1062347 = 11 * 13 * 17 * 19 * 23;
%C A271630 30808063 = 11 * 13 * 17 * 19 * 23 * 29;
%C A271630 955049953 = 11 * 13 * 17 * 19 * 23 * 29 * 31;
%C A271630 35336848261 = 11 * 13 * 17 * 19 * 23 * 29 * 31 * 37;
%C A271630 1448810778701 = 11 * 13 * 17 * 19 * 23 * 29 * 31 * 37 * 41; etc.
%H A271630 Paolo P. Lava, <a href="/A271630/b271630.txt">Table of n, a(n) for n = 1..10000</a>
%H A271630 Paolo P. Lava, <a href="/A271630/a271630.txt">First 500 palindromes in the sequence</a>
%H A271630 Paolo P. Lava, <a href="/A271630/a271630_1.txt">First 10000 non palindromes whose reverses are terms of the sequence</a>
%e A271630 343 is coprime to:
%e A271630 43, 143, 243, 443, 543, 643, 743, 843, 943 (where the MSD has been changed);
%e A271630 303, 313, 323, 333, 353, 363, 373, 383, 393 (where the '4' in the middle has been changed);
%e A271630 340, 341, 342, 344, 345, 346, 347, 348, 349 (where the LSD has been changed) .
%p A271630 with(numtheory); P:=proc(q) local a,j,k,n,ok;
%p A271630 for n from 2 to q do if not isprime(n) then ok:=1; j:=0;
%p A271630 while ok=1 and j<9 do j:=j+1; for k from 1 to ilog10(n)+1 do
%p A271630 a:=trunc(n/10^k)*10^k+((trunc((n mod 10^k)/10^(k-1))-j) mod 10)*10^(k-1)+(n mod 10^(k-1));
%p A271630 if gcd(n,a)>1 then ok:=0; break; fi; od; od;
%p A271630 if ok=1 then print(n); fi; fi; od; end: P(10^5);
%t A271630 Select[Range[10^3], Function[n, And[CompositeQ@ n, AllTrue[Flatten@ Function[w, Map[Function[k, Map[FromDigits[ReplacePart[w, k -> #]] &, Range[0, 9]]], Range@ Length@ w] /. m_ /; m == n -> Nothing]@ IntegerDigits@ n, CoprimeQ[#, n] &]]]] (* _Michael De Vlieger_, Apr 15 2016 *)
%Y A271630 Cf. A038510, A038511, A078972.
%K A271630 nonn,easy,base
%O A271630 1,1
%A A271630 _Paolo P. Lava_, Apr 14 2016