A379143 Lexicographically earliest sequence of distinct positive integers such that both the sum of terms a(1)..a(n) and the sum of the digits in these terms is a prime number.

2, 3, 6, 8, 4, 24, 20, 42, 22, 48, 44, 28, 26, 40, 114, 68, 64, 176, 82, 66, 80, 46, 84, 192, 110, 60, 138, 156, 118, 62, 136, 174, 134, 154, 200, 172, 158, 130, 132, 194, 222, 178, 86, 88, 150, 116, 246, 190, 228, 206, 244, 152, 204, 112, 264, 170, 196, 288, 866, 240, 208, 248, 312, 268, 242, 198, 282, 286, 266, 354, 220, 284, 262, 224, 280, 260, 330, 226

Offset

1,1

Comments

As the sum of terms beyond a(2) = 3 must be odd, a(2) is the only odd term. Is is unknown if all even numbers appear.

Similarly, the sum of digits of terms beyond a(2) must be odd, so a(2) is the only term with odd sum of digits. 10 is the first even number that does not appear. - Michael S. Branicky, Dec 18 2024

Links

Scott R. Shannon, Table of n, a(n) for n = 1..5000

Example

a(5) = 4 as the sum of both the terms and digits from a(1)..a(5) is 23, which is a prime number, and 4 has not previously appeared.
a(6) = 24 as the sum of terms from a(1)..a(6) is 47 while the sum of digits of these terms is 29, and both 47 and 29 are prime numbers while 24 has not previously appeared.

Prog

(Python)
from sympy import isprime
from itertools import count, islice
def sod(n): return sum(map(int, str(n)))
def agen(): # generator of terms
    aset, s, ds, m = {2, 3}, 5, 5, 4
    yield from [2, 3]
    while True:
        an = next(k for k in count(m, 2) if k not in aset and all(isprime(i) for i in [s+k, ds+sod(k)]))
        s, ds = s+an, ds+sod(an)
        aset.add(an)
        yield an
        while m in aset or sod(m)&1: m += 2
print(list(islice(agen(), 80))) # Michael S. Branicky, Dec 18 2024

Crossrefs

Cf. A000040, A379142, A007953, A000217, A320081.

Sequence in context: A349917 A191453 A191454 * A276955 A276945 A246266

Adjacent sequences: A379139 A379140 A379142 * A379144 A379146 A379148

Keyword

nonn,base,new

Author

Scott R. Shannon, Dec 16 2024

Status

approved