OFFSET
1,1
COMMENTS
Only numbers ending in 1, 3, 7 and 9.
Apart from the first 10 terms, A078972 is a subset of this sequence.
Subsequence of A038510. - Altug Alkan, Apr 15 2016
Least squareless numbers with increasing number of primes:
143 = 11 * 13;
2431 = 11 * 13 * 17;
45353 = 7 * 11 * 19 * 31;
1062347 = 11 * 13 * 17 * 19 * 23;
30808063 = 11 * 13 * 17 * 19 * 23 * 29;
955049953 = 11 * 13 * 17 * 19 * 23 * 29 * 31;
35336848261 = 11 * 13 * 17 * 19 * 23 * 29 * 31 * 37;
1448810778701 = 11 * 13 * 17 * 19 * 23 * 29 * 31 * 37 * 41; etc.
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..10000
Paolo P. Lava, First 500 palindromes in the sequence
EXAMPLE
343 is coprime to:
43, 143, 243, 443, 543, 643, 743, 843, 943 (where the MSD has been changed);
303, 313, 323, 333, 353, 363, 373, 383, 393 (where the '4' in the middle has been changed);
340, 341, 342, 344, 345, 346, 347, 348, 349 (where the LSD has been changed) .
MAPLE
with(numtheory); P:=proc(q) local a, j, k, n, ok;
for n from 2 to q do if not isprime(n) then ok:=1; j:=0;
while ok=1 and j<9 do j:=j+1; for k from 1 to ilog10(n)+1 do
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));
if gcd(n, a)>1 then ok:=0; break; fi; od; od;
if ok=1 then print(n); fi; fi; od; end: P(10^5);
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Paolo P. Lava, Apr 14 2016
STATUS
approved