A086578
a(n) = 7*(10^n - 1).
Original entry on oeis.org
0, 63, 693, 6993, 69993, 699993, 6999993, 69999993, 699999993, 6999999993, 69999999993, 699999999993, 6999999999993, 69999999999993, 699999999999993, 6999999999999993, 69999999999999993, 699999999999999993, 6999999999999999993, 69999999999999999993, 699999999999999999993
Offset: 0
One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1:
A002283, m=2:
A086573, m=3:
A086574, m=4:
A086575, m=5:
A086576, m=6:
A086577, m=7:
A086578, m=8:
A086579, m=9:
A086580.
A100413
Numbers k such that k is reversal(k)-th even composite number (k is A004086(k)-th even composite number).
Original entry on oeis.org
52, 592, 5992, 59992, 599992, 5999992, 59999992, 599999992, 5999999992, 59999999992, 599999999992, 5999999999992, 59999999999992, 599999999999992, 5999999999999992, 59999999999999992, 599999999999999992
Offset: 1
592 is in the sequence because 592 is the 295th even composite number.
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[6*10^n -8: n in [1..20]]; // G. C. Greubel, Apr 13 2023
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A100413:=n->6*10^n-8; seq(A100413(n), n=1..20); # Wesley Ivan Hurt, Apr 06 2014
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Table[6*10^n-8, {n,20}]
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A100413(n):=6*10^n-8$
makelist(A100413(n),n,1,17); /* Martin Ettl, Nov 08 2012 */
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Vec(4*x*(5*x+13)/((x-1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Oct 14 2014
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[6*10^n -8 for n in range(1,21)] # G. C. Greubel, Apr 13 2023
A169830
Numbers k such that 2*reverse(k) - k = 1.
Original entry on oeis.org
1, 73, 793, 7993, 79993, 799993, 7999993, 79999993, 799999993, 7999999993, 79999999993, 799999999993, 7999999999993, 79999999999993, 799999999999993, 7999999999999993, 79999999999999993, 799999999999999993, 7999999999999999993, 79999999999999999993, 799999999999999999993
Offset: 1
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k = 1; lst = {}; fQ[n_] := 2 FromDigits@ Reverse@ IntegerDigits@n == 1 + n; While[k < 10^8, If[fQ@k, Print@k; AppendTo[lst, k]]; k++ ]; lst (* Robert G. Wilson v, Jun 01 2010 *)
Rest@ CoefficientList[Series[x (1 + 62 x)/((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* or *)
Table[If[n == 1, 1, FromDigits@ Join[{7}, ConstantArray[9, n - 2], {3}]], {n, 20}] (* or *)
LinearRecurrence[{11, -10}, {1, 73}, 20] (* Michael De Vlieger, Feb 12 2017 *)
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isok(n) = 2*fromdigits(Vecrev(digits(n))) - n == 1; \\ Michel Marcus, Feb 12 2017
A100414
Numbers n such that n is R(n)-th composite number where R(n) is the digit reversal of n (A002808(A004086(n))=n).
Original entry on oeis.org
21, 48034, 69926, 180461, 214591, 409473, 563715, 41630193, 253385633342, 661494322636
Offset: 1
41630193 is in the sequence because 41630193 is the 39103614th composite number.
A136543
Numbers n such that phi(n)+sigma(n)=4*reversal(n).
Original entry on oeis.org
793, 79993, 2152311, 79999993, 7999999993, 799999999993
Offset: 1
phi(2152311)+sigma(2152311)=1217664+3312384=4*1132512=4*reversal(2152311), so 2152311 is in the sequence.
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Do[If[4*FromDigits@Reverse@IntegerDigits@n==EulerPhi@n+ DivisorSigma[1,n],Print[n]],{n,100000000}]
A384597
Integers k such that k + 1 has a divisor that is an anagram of k, which must have the same number of digits as k.
Original entry on oeis.org
1, 41, 73, 631, 793, 6031, 6391, 6733, 7412, 7520, 7993, 8627, 9710, 25147, 37112, 43916, 49316, 51427, 60031, 60391, 60733, 62314, 63214, 63991, 66331, 67393, 67933, 70211, 71132, 72101, 74102, 74912, 75020, 75290, 78260, 79993, 81103, 85712, 86927, 89627
Offset: 1
73 is in this sequence since 73 + 1 = 37*2, where 37 is an anagram of 73.
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{1}~Join~Select[Range[100000],ContainsAny[IntegerDigits/@Divisors[#+1],Complement[Permutations[IntegerDigits[#]],{IntegerDigits[#]}]]&] (* James C. McMahon, Jun 10 2025 *)
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isok(k) = my(s=vecsort(digits(k))); fordiv(k+1, d, if (vecsort(digits(d)) == s, return(1))); \\ Michel Marcus, Jun 04 2025
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def ok(k):
return any((k+1)%d==0 and sorted(str(d))==sorted(str(k)) and len(str(d))==len(str(k)) for d in range(1,k+2))
print(", ".join(map(str, [k for k in range(1, 100000) if ok(k)])))
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