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 A363248 Nonprime base-10 palindromes whose arithmetic derivative is a base-10 palindrome. 0
 0, 1, 4, 6, 9, 121, 222, 717, 989, 1331, 10201, 13231, 15251, 15751, 15851, 18281, 19291, 28882, 28982, 31613, 34043, 35653, 37073, 37673, 37873, 38383, 38683, 40304, 41814, 50405, 97079, 98789, 99899, 536635, 913319, 980089, 1030301, 1115111, 1226221, 1336331, 1794971, 2630362, 2882882, 3303033 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Nonprime members k of A002113 such that A003415(k) is also in A002113. A003415(p) = 1 is a palindrome for all primes p. It seems that most members of A363246 are primes. LINKS Table of n, a(n) for n=1..44. EXAMPLE a(7) = 222 is a term because it is a palindrome, is not prime, and its arithmetic derivative 191 is a palindrome. MAPLE ader:= proc(n) local t; n*add(t[2]/t[1], t=ifactors(n)[2]) end proc: rev:= proc(n) local L, i; L:= convert(n, base, 10); add(L[-i]*10^(i-1), i=1..nops(L)) end proc: palis:= proc(d) local x, y; if d::even then seq(10^(d/2)*x+rev(x), x=10^(d/2-1)..10^(d/2)-1) else seq(seq(10^((d+1)/2)*x+10^((d-1)/2)*y+rev(x), y=0..9), x=10^((d-3)/2) ..10^((d-1)/2)-1) fi end proc: palis(1):= \$0..9: filter:= proc(n) local d; if isprime(n) then return false fi; d:= ader(n); d = rev(d) end proc: select(filter, [seq(palis(i), i=1..7)]); CROSSREFS Cf. A002113, A003415. Complement of A002385 in A363246. Sequence in context: A245044 A104389 A115655 * A084350 A028279 A114743 Adjacent sequences: A363245 A363246 A363247 * A363249 A363250 A363251 KEYWORD nonn,base AUTHOR Robert Israel, May 23 2023 STATUS approved

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Last modified August 15 01:27 EDT 2024. Contains 375171 sequences. (Running on oeis4.)