A340064 Every odd term k of the sequence is the cumulative sum of the prime digits used so far (the digits of k are included in the sum).

3, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 9, 22, 24, 26, 28, 19, 21, 30, 32, 34, 36, 38, 40, 42, 43, 44, 46, 48, 50, 52, 54, 63, 73, 56, 58, 60, 62, 64, 66, 68, 70, 72, 101, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 131, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 141, 126, 128, 153

Offset

1,1

Comments

This is the lexicographically earliest sequence of distinct positive terms with this property. The prime digits are 2, 3, 5 and 7.

The sequence is first extended with the smallest odd term not leading to a contradiction; if no such term exists, the sequence is extended with the smallest even term not yet present.

Links

Table of n, a(n) for n=1..75.

Example

Not a(1) = 1 as this 1, being odd, should be the sum of the prime digits so far -- which is wrong (there are none);
not a(1) = 2 as a(1) = 3 is odd and possible here;
a(12) = 9 as 9 is odd and the sum of the prime digits 3 + 2 + 2 + 2;
a(13) = 22 as 22 is the smallest even term available;
a(17) = 19 as 19 = 3 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2;
a(18) = 21 as 21 is the sum of 19 + 2 (the first digit of 21 itself); etc.

Prog

(Python)
def pds(k): return sum(int(d) for d in str(k) if d in "2357")
def aupto(nn):
  aset, alst, primesum, nexteven = set(), [], 0, 2
  for n in range(1, nn):
    k = 1
    found = False
    while not found:
      while k in aset: k += 2
      if k == primesum + pds(k): found = True; break
      if k > primesum + 7 * len(str(k)): break
      k += 2
    if found: ak = k
    else: ak = nexteven; nexteven += 2
    aset.add(ak); alst.append(ak); primesum += pds(ak)
  return alst
print(aupto(76)) # Michael S. Branicky, Dec 29 2020

Crossrefs

CF. A338924

Sequence in context: A349472 A195208 A114651 * A240539 A138245 A163328

Adjacent sequences: A340061 A340062 A340063 * A340065 A340066 A340067

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Dec 28 2020

Status

approved