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

121, 143, 169, 187, 209, 221, 247, 253, 289, 299, 319, 323, 341, 343, 361, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 529, 533, 551, 553, 559, 583, 589, 611, 629, 649, 667, 671, 689, 697, 703, 713, 731, 737, 767, 779, 781, 793, 799, 803, 817, 841, 851

Offset: 1

Author

Paolo P. Lava, Apr 14 2016

Keywords

• nonn
• easy
• base

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.

Examples

			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) .
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000
• Paolo P. Lava, First 500 palindromes in the sequence
• Paolo P. Lava, First 10000 non palindromes whose reverses are terms of the sequence

Crossrefs

Cf. A038510, A038511, A078972.

Programs

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 *)