The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A316412 Positive numbers m so that deletion of some or none but not all digits from m yields a noncomposite number. 0

%I

%S 1,2,3,5,7,11,13,17,23,31,37,53,71,73,113,131,137,173,311,317

%N Positive numbers m so that deletion of some or none but not all digits from m yields a noncomposite number.

%C Subsequence of A068669. It is easy to see that these are the only terms from the said sequence that satisfy our definition; there are no more terms < 10000. If there is one >= 10000 then there would be one in [1000, 9999]. A contradiction hence the sequence is finite and full.

%C Also noncomposites m (in base 10) for which the concatenation of every subsequence of digits of m is noncomposite (in base 10). - _David A. Corneth_, Aug 08 2018

%e 317 is a member since all its subsequences, i.e., 3, 1, 7, 31, 17, 37, 317, are noncomposite.

%e 313 is not a member since one of its subsequences (33) is composite.

%t Select[Range[10^3], AllTrue[FromDigits /@ Union@ Rest@ Subsets@ IntegerDigits@ #, ! CompositeQ@ # &] &] (* _Michael De Vlieger_, Aug 05 2018 *)

%o (C++)

%o #include <iostream>

%o #include <queue>

%o int main() {

%o int upper = 1000;

%o // 0->composite, 1->prime, 2->member of the sequence

%o auto *nums = new int[upper];

%o for (int i = 0; i < upper; i++)

%o nums[i] = 1;

%o nums = nums = 2;

%o std::queue<int> in_progress;

%o in_progress.push(1);

%o for (int i = 2; i < upper; i++) {

%o if (nums[i] == 0) continue;

%o // is a prime

%o in_progress.push(i);

%o for (int j = i + i; j < upper; j += i) {

%o nums[j] = 0;

%o }

%o }

%o while (!in_progress.empty()) {

%o int p = in_progress.front();

%o in_progress.pop();

%o int div = 1;

%o bool valid = true;

%o while (div <= p) {

%o int del = (p / (div * 10)) * div + (p % div);

%o if (nums[del] != 2) {

%o valid = false;

%o break;

%o }

%o div *= 10;

%o }

%o if (valid) {

%o nums[p] = 2;

%o std::cout << p << ", ";

%o }

%o }

%o }

%Y Subsequence of A068669.

%Y Cf. A008578.

%K base,easy,fini,full,nonn

%O 1,2

%A _Matej Kripner_, Aug 04 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)