This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
import Data.List ((\\)) a230959 n = (if null cds then 0 else read cds) :: Integer where cds = "9876543210" \\ show n
pd[n_]:=Module[{idn=Sort[IntegerDigits[n]]},If[idn==Range[0,9],0,FromDigits[ Reverse[ Complement[ Range[ 0,9],idn]]]]]; Table[pd[n],{n,0,30}] (* Harvey P. Dale, Nov 16 2023 *)
def A230959(n): return int(''.join(sorted(set('9876543210')-set(str(n)),reverse=True)) or 0) # Chai Wah Wu, Nov 23 2022
987654323 is a prime and appears in the sequence because 987654323 = 2 + 987654321. 987654337 is a prime and appears in the sequence because 987654337 = 16 + 987654321.
KD := proc() local a; a:=n+987654321; if isprime(a) then RETURN (a); fi; end: seq(KD(), n=1..1000);
Select[Table[k + 987654321, {k,1,1000}], PrimeQ]
c=0; a=n+987654321; Do[If[PrimeQ[a], c=c+1; Print[c," ",a]], {n,0,200000}] (* b-file *)
Denote by F(1,P) the Fibonacci type sequence x(n+1) = x(n) + x(n-1) with x(0) = 1, x(1) = P. Then for P = a(8) = 9530359, F(1,P) = (1, 9530359, 9530360, 19060719, 28591079, 47651798, 76242877, 123894675, ...) where a 9-digits anagram has occurred.
A034306=[p | p<-[A002113(n) | n<-[1..6*10^4]], is_A034587(p)] \\ All 68 terms in a fraction of a second. - M. F. Hasler, Jan 08 2020
Denote by F(a,b) the Fibonacci-type sequence x(n+1) = x(n) + x(n-1) starting with x(0) = a, x(1) = b. Then F(1,21998) = (1, 21998, 21999, 43997, 65996, 109993, 175989, 285982, 461971, 747953, 1209924, 1957877, 3167801, 5125678, 8293479, 13419157, 21712636, 35131793, 56844429, 91976222, 148820651, 240796873, 389617524, ...) where a nine-digits anagram has been reached. The growth is roughly linear in three parts, with a slope of 700 up to a(292967) = 206993812, then an average slope of 1130 before it rises to (9.87e8 - 4.94e8)/2.05e5 ~ 2400 for 546211 <= n <= 750767 (cf. formula & comments): a(100) = 71960, a(200) = 149540, a(500) = 351868, a(1000) = 649921, a(2000) = 1400539, a(5000) = 3209798, a(10^4) = 6595301, a(2e4) = 13351498, a(5e4) = 32441506, a(10^5) = 67090523, a(2e5) = 134759627, a(3e5) = 214973567, a(4e5) = 327136594, a(5e5) = 439256717. - _M. F. Hasler_, Jan 07 2020
A034587=select( {is_A034587(n,s=1,L=[1..9])=while( 123456789 > n=s+s=n,); n<1e9 && until( 987654321 < n=s+s=n, Set(digits(n))==L&&return(n))}, [1..22222]) \\ Function is_A034587 returns the 9-digit anagram if one is reached; null == false == 0 else. nxt_A034587(n)={until(is_A034587(n+=1),);n} \\ Returns next larger term A034587(n)={if(n>546210, A050289(n-387887)-1, #A034587>=n, A034587[n], A034587=concat( A034587, vector(n-#A034587,i, n=nxt_A034587(if(i>1,n,A034587[#A034587])))); n)} \\ Uses the two functions above. Could use Vecsmall(...) in definition of A034587 and vectorsmall in A034587(n) to reduce memory. \\ M. F. Hasler, Jan 06 2020 and Jan 07 2020
def ok(n):
f, g = n, n+1
while g < 10**9:
if g > 123456788 and "".join(sorted(str(g))) == "123456789":
return True
f, g = g, f+g
return False
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, Feb 18 2024
Starting with (1, 233419), Fibonacci iterations x(n+1) = x(n) + x(n-1) yield the sequence (1, 233419, 233420, 466839, 700259, 1167098, 1867357, 3034455, 4901812, 7936267, 12838079, 20774346, 33612425, 54386771, 87999196, 142385967, ...) where a nine-digits anagram is reached.
select( is_A034587, primes(22222)) \\ or, if a vector A034587 is available: select(isprime, A034587) \\ e.g., using b034587.txt. - M. F. Hasler, Jan 06 2020
Denote by F(1, N) the Fibonacci sequence x(k+1) = x(k) + x(k-1) starting with x(0) = 1, x(1) = N. Then for N = 228631, F(1, N) = (1, 228631, 228632, 457263, 685895, 1143158, 1829053, 2972211, 4801264, 7773475, 12574739, 20348214, 32922953, 53271167, 86194120, 139465287, ...), where a nine-digits anagram has been reached.
A034589_upto(N)=[n|n<-A000959_upto(N),is_A034587(n)] \\ or select(is_A034587, A959=from("b000959.txt")). - M. F. Hasler, Jan 10 2020
1234567891 is a prime and appears in the sequence because 1234567891 = 1^2 + 1234567890. 1234568059 is a prime and appears in the sequence because 1234568059 = 13^2 + 1234567890.
KD := proc() local a; a:=n^2+1234567890; if isprime(a) then RETURN (a); fi; end: seq(KD(), n=1..2000);
Select[Table[k^2+1234567890,{k,1,2000}],PrimeQ]
c=0; a=n^2+1234567890; Do[If[PrimeQ[a],c=c+1; Print[c," ",a]], {n,0,200000}] (*b-file*)
for(n=1,10^4,if(ispseudoprime(10^n - 123456789),print1(n,", ")))
[n: n in [1..500] | IsPrime(10^n+987654321)]; // Vincenzo Librandi, Oct 12 2014
Select[Range[1000], PrimeQ[10^# + 987654321] &] (* Vincenzo Librandi, Oct 12 2014 *)
for(n=1,10^4,if(ispseudoprime(10^n+987654321),print1(n,", ")))
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