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 A360504 Concatenate the ternary strings for 1,2,...,n-1, n, n-1, ..., 2,1. 3
 1, 121, 121021, 1210111021, 12101112111021, 121011122012111021, 1210111220212012111021, 12101112202122212012111021, 1210111220212210022212012111021, 1210111220212210010110022212012111021, 1210111220212210010110210110022212012111021, 1210111220212210010110211010210110022212012111021 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If the terms are read as ternary strings and converted to base 10, we get A260853. For example, a(3) = 121021_3 = 439_10, which is A260853(3). This is a prime. What is the next prime term? If the terms are read as decimal numbers, which of them are primes? a(3) = 121021_10 is a decimal prime, but what is the next one? It is a surprise that 121021 is a prime in both base 3 and base 10. LINKS Winston de Greef, Table of n, a(n) for n = 1..123 Index entries for sequences related to Most Wanted Primes video EXAMPLE To get a(3) we concatenate 1, 2, 10, 2, and 1, getting 121021. MAPLE t:= n-> (l-> parse(cat(seq(l[-i], i=1..nops(l)))))(convert(n, base, 3)): a:= n-> parse(cat(map(t, [\$1..n, n-i\$i=1..n-1])[])): seq(a(n), n=1..12); # Alois P. Heinz, Feb 17 2023 MATHEMATICA Table[FromDigits[Flatten[Join[IntegerDigits[#, 3]&/@Range[n], IntegerDigits[#, 3]&/@ Range[ n-1, 1, -1]]]], {n, 20}] (* Harvey P. Dale, Oct 01 2023 *) PROG (Python) from sympy.ntheory import digits def a(n): return int("".join("".join(map(str, digits(k, 3)[1:])) for k in list(range(1, n+1))+list(range(n-1, 0, -1)))) print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Feb 18 2023 (Python) # faster version for initial segment of sequence from sympy.ntheory import digits from itertools import count, islice def agen(): # generator of terms sf, sr = "", "" for n in count(1): sn = "".join(map(str, digits(n, 3)[1:])) sf += sn yield int(sf + sr) sr = sn + sr print(list(islice(agen(), 15))) # Michael S. Branicky, Feb 18 2023 CROSSREFS Cf. A007089, A360502, A360503. This is the ternary analog of A173426. Sequence in context: A202887 A195275 A082489 * A028463 A013749 A178192 Adjacent sequences: A360501 A360502 A360503 * A360505 A360506 A360507 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Feb 17 2023 STATUS approved

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Last modified June 17 00:51 EDT 2024. Contains 373432 sequences. (Running on oeis4.)