A260597 Primes as they occur for the first time as factors of terms of A173426 = concatenation(1,2,...,n,n-1,...,1).

11, 3, 37, 101, 41, 271, 7, 13, 239, 4649, 73, 137, 333667, 12345678910987654321, 17636684157301569664903, 2799473675762179389994681, 1109, 4729, 2354041513534224607850261, 571, 3167, 10723, 439781, 2068140300159522133, 75401, 687437, 759077450603

Offset

1,1

Comments

Or, distinct elements of A260589 in the order they occur for the first time.

Links

M. F. Hasler and Chai Wah Wu, Table of n, a(n) for n = 1..114 (a(n) for n = 1..84 from M. F. Hasler)

Example

A173426(1) = 1;  A173426(2) = 121 = 11^2 => a(1) = 11.
A173426(3) = 12321 = 3^2 37^2 => a(2..3) = (3, 37).
A173426(4) = 1234321 = 11^2 101^2 => a(4) = 101.
A173426(5) = 123454321 = 41^2 271^2 => a(5..6) = (41, 271).
A173426(6) = 12345654321 = 3^2 7^2 11^2 13^2 37^2 => a(7..8) = (7, 13).

Prog

(PARI) S=[]; apply(t->S=setunion(S, t=setminus(Set(t), S)); t, vector(30, n, A260589_row(n)))
(Python)
from sympy import primefactors
A260597_list = []
for n in range(1, 10):
    m = primefactors(int(''.join([str(d) for d in range(1, n+1)]+[str(d) for d in range(n-1, 0, -1)])))
    for p in m:
        if not p in A260597_list:
            A260597_list.append(p) # Chai Wah Wu, Aug 11 2015

Crossrefs

Sequence in context: A298927 A102380 A204845 * A147555 A157883 A038317

Adjacent sequences: A260594 A260595 A260596 * A260598 A260599 A260600

Keyword

nonn

Author

M. F. Hasler, Jul 29 2015

Status

approved