A114316 Lexicographically earliest sequence of positive distinct terms such that the a(n)th digit of the sequence is nonprime (see the Comments section).

1, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 27, 38, 40, 41, 37, 39, 45, 46, 48, 49, 50, 51, 52, 53, 55, 57, 66, 67, 68, 70, 71, 73, 75, 80, 81, 82, 83, 84, 86, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 104, 105, 106

Offset

1,2

Comments

"Nonprime" digits are 0, 1, 4, 6, 8 and 9.

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Example

Nonprime digits are between brackets:
Sequence: (1),3,(4),(6),7,(8),(9),(1)(0),(1)(1),(1)2,(1)4, ...
Digit position in the sequence: 1st, 3rd, 4th, 6th, 7th, 8th, 9th, 10th, 11th, 12th, 14th, ... = a reordering of the sequence itself.

Prog

(Python)
nonprime = [0, 1, 4, 6, 8, 9]
terms = [1, 3, 4, 6, 7, 8, 9]
def si(test_list):#all terms greater than 0 and no repetitions
  a = all(i > 0 for i in test_list)
  b = len(test_list) == len(set(test_list))
  return a & b
def clear(test_list):#sequence meets definitional criteria
  full = (''.join(str(x) for x in test_list))
  for a in test_list:
      if int(a)-1 >= len(full):
          return True
      elif int(full[int(a)-1]) not in nonprime:
          return False
  return True
while len(terms) < 1000:
  start = 1
  while True:
      terms.append(start)
      if si(terms) and clear(terms):
          break
      else:
          terms.pop()
          start += 1
# David Consiglio, Jr., Oct 30 2023

Crossrefs

Cf. A114319 (same idea but with the "noncomposite" digits 0, 1, 2, 3, 5 and 7).

Sequence in context: A092460 A092459 A039232 * A039176 A066533 A039130

Adjacent sequences: A114313 A114314 A114315 * A114317 A114318 A114319

Keyword

nonn,base

Author

Eric Angelini, Feb 05 2006

Extensions

Corrected and extended by R. J. Mathar, Bernard Schott and Eric Angelini

a(63) and beyond from David Consiglio, Jr., Oct 30 2023

Status

approved