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

1,1

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

Paolo P. Lava, First 10000 non palindromes whose reverses are terms of 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

Cf. A038510, A038511, A078972.

Sequence in context: A020253 A182776 A080466 * A038511 A285784 A062649

Adjacent sequences: A271627 A271628 A271629 * A271631 A271632 A271633

Keyword

nonn,easy,base

Author

Paolo P. Lava, Apr 14 2016

Status

approved