A217399 -id:A217399 - cp's OEIS frontend

A320862 Powers of 2 with initial digit 6.

64, 65536, 67108864, 68719476736, 604462909807314587353088, 618970019642690137449562112, 633825300114114700748351602688, 649037107316853453566312041152512, 664613997892457936451903530140172288, 680564733841876926926749214863536422912

Offset: 1

Muniru A Asiru, Oct 23 2018

Muniru A Asiru, Table of n, a(n) for n = 1..220
Index to divisibility sequences

Cf. A000079 (powers of 2), A008952 (leading digit of 2^n), A217399 (numbers starting with 6).

Powers of 2 with initial digit k, (k = 1..6): A067488, A067480, A320859, A320860, A320861, this sequence.

Filtered(List([0..180],n->2^n),i->ListOfDigits(i)[1]=6);

[2^n: n in [1..160] | Intseq(2^n)[#Intseq(2^n)] eq 6]; // G. C. Greubel, Oct 27 2018

select(x->"6"=""||x[1],[2^n$n=0..180])[];

Select[2^Range[160], First[IntegerDigits[#]] == 6 &] (* G. C. Greubel, Oct 27 2018 *)

select(x->(digits(x)[1]==6), vector(200, n, 2^n)) \\ Michel Marcus, Oct 26 2018

A341909 a(0) = 0; for n > 0, a(n) is the smallest positive integer not yet in the sequence such that the first digit of a(n) differs by 1 from the last digit of a(n-1).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 80, 10, 11, 20, 12, 13, 21, 22, 14, 30, 15, 40, 16, 50, 17, 60, 18, 70, 19, 81, 23, 24, 31, 25, 41, 26, 51, 27, 61, 28, 71, 29, 82, 32, 33, 42, 34, 35, 43, 44, 36, 52, 37, 62, 38, 72, 39, 83, 45, 46, 53, 47, 63, 48, 73, 49, 84, 54, 55, 64, 56, 57, 65, 66, 58, 74, 59

Offset: 0

Scott R. Shannon, Feb 23 2021

			a(10) = 80 as the last digit of a(9) = 9 is 9, thus the first digit of a(10) must be 8. As 8 has already been used the next smallest number starting with 8 is 80.
a(16) = 21 as the last digit of a(15) = 13 is 3, thus the first digit of a(16) must be 2 or 4. As 2, 4 and 20 have already been used the next smallest number starting with 2 is 21.

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Cf. A001477, A000027, A341692, A341002, A331163, A331375.

Cf. A131835, A217394, A217395, A217397, A217398, A217399, A217400, A217401, A217402.

Block[{a = {0}, k}, Do[k = 1; While[Nand[FreeQ[a, k], Abs[First@ IntegerDigits[k] - Mod[a[[-1]], 10]] == 1], k++]; AppendTo[a, k], {i, 76}]; a] (* Michael De Vlieger, Feb 23 2021 *)

def nextd(strn, d):
  n = int(strn) if strn != "" else 0
  return n+1 if str(n+1)[0] == str(d) else int(str(d)+'0'*len(strn))
def aupton(term):
  alst, aset = [0], {0}
  lastdstr = ["" for d in range(10)]
  for n in range(1, term+1):
    lastdig = alst[-1]%10
    firstdigs = set([max(lastdig-1, 0), min(lastdig+1, 9)]) - {0}
    cands = [nextd(lastdstr[d], d) for d in firstdigs]
    m = min(cands)
    argmin = cands.index(m)
    alst.append(m)
    strm = str(m)
    lastdstr[int(strm[0])] = strm
  return alst
print(aupton(76)) # Michael S. Branicky, Feb 23 2021

cp's OEIS Frontend

A320862 Powers of 2 with initial digit 6.

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