A322919 Numbers k such that k and k-1 both first appear in the same power of 2 (in base 10).

59, 74, 111, 785, 793, 914, 957, 985, 1070, 1467, 2019, 2099, 2332, 2610, 2934, 3028, 3083, 3311, 3334, 3973, 4198, 4208, 4334, 4590, 4689, 4785, 5247, 5350, 5535, 6166, 6335, 6669, 6761, 7167, 7340, 7707, 7980, 8668, 8990, 9180, 9840, 11110, 13096, 16285, 17418, 18091, 18361, 19219, 20522, 21494, 21827

Offset: 1

Author

Keith F. Lynch, Dec 30 2018

Keywords

• nonn
• base

Examples

			For instance 2019 is in the sequence since 2018 and 2019 both appear in 2^212 and neither appear in any smaller power of two.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..3106

Crossrefs

Indices of consecutive repeats in A030000.

Programs

C

#include 
int main() {
  int n = 1000001;  /* Highest term */
  int p = 2;        /* Powers of two.  Test throughly if you change it. */
  int r = 10;       /* Base ten.  Test throughly if you change it. */
  char a[n];
  int b,c,i,j,k,k2,l,lk,m,ok,ok2,u,d[7],f[n],g[n],v[n];
  u = n;
  for (j=0;jM. F. Hasler, Jul 05 2021*/
    f[j] = g[j] = -1;
  }
  a[0] = 1;
  for (m=0;(m-1;l--) {
          ok = 1;
          for (j=lk-1;j>-1;j--) if (a[l+j] != d[j]) ok = 0;
          if (ok) ok2 = 1;
        }
        if (ok2) {
          f[k] = m;
          u--;
        }
      }
      if ((g[k]==-1) && (lk<=b+1)) {
        ok = 1;
        for (j=lk-1;j>-1;j--) if (a[b-lk+j+1] != d[j]) ok = 0;
        if (ok) g[k] = m;
      }
    }
    c = 0;
    for (j=0;j r-1) {
        c = a[j] / r;
        a[j] %= r;
      }
    }
  }
  for (i=1;i
				

PARI

uptoQdigits(n) = {v = vector(10^n); p = 1/2; todo = 10^n; my(res = List());
for(i = 1, oo, p<<=1; process(p, n); if(todo <= 0, break)); for(i = 1, #v - 1,
if(v[i] == v[i+1], listput(res, i))); res}
process(p, n) = {my(dp = digits(p), vd, lp = logint(p, 2)); qdp = #dp; my(t = min(n, qdp)); for(qd = 1, t, for(j = 1, qdp - qd + 1, vd = fromdigits(vector(qd, i, dp[j+i-1])); if(v[vd + 1] == 0, v[vd + 1] = lp; todo--)))} \\ David A. Corneth, Dec 31 2018