A073729 -id:A073729 - cp's OEIS frontend

A073731 Least k such that A073729(k) = n.

10, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 3, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 4, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 5, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 6, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 7, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 8, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 9

Offset: 10

Reinhard Zumkeller, Aug 05 2002

The sequence is finite as 10 <= A073729(n) <= 99 for all n; a(n) = (if n mod 11 > 0 then n else n mod 10) for 10<=n<=99: the range is {n | 1<=n<=99}.

a(n) = n mod 10 + signum(n mod 11) * (n - n mod 10) for 10<=n<=99.

A138843 Concatenation of initial and final digits of n-th perfect number.

Original entry on oeis.org

66, 28, 46, 88, 36, 86, 18, 28, 26, 16, 18, 18, 26, 18, 58, 18, 96, 36, 16, 48, 16, 56, 36, 96, 16, 86, 36, 18, 18, 16, 28, 18, 86, 88, 36, 16, 86, 96, 46

Offset: 1

Omar E. Pol, Apr 02 2008

Also, concatenation of A135617(n) and A094540(n).

			a(5)=36 because the 5th perfect number A000396(5) is 33550336 and the concatenation of initial and final digits of 33550336 is 36.

Cf. A000396, A073729, A135617, A094540, A138840, A138841, A138842, A138844.

A138840 Concatenation of initial and final digits of n-th prime.

Original entry on oeis.org

22, 33, 55, 77, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 11, 13, 17, 19, 13, 17, 11, 17, 19, 19, 11, 17, 13, 17, 13, 19, 11, 11, 13, 17, 19, 21, 23, 27, 29, 23, 29, 21, 21, 27, 23, 29, 21, 27, 21, 23, 23, 37, 31, 33, 37, 31, 37, 37

Offset: 1

Omar E. Pol, Apr 01 2008

There are only 38 distinct terms in this sequence, all of them odd with the exception of 22. 55 is the only term divisible by 5. 22 and 55 each appear only once. The other terms, each of which appears multiple times, are the odd two-digit numbers not divisible by 5. - Harvey P. Dale, May 15 2012

a(n) is the concatenation of A077648(n) and A007652(n), hence all terms of this sequence have two digits in the same way as A073729. - Omar E. Pol, Mar 23 2018

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A007652, A073729, A077648, A138841, A138842, A138843, A138844.

Cf. A137589 (same except for first four terms).

a:= n-> (p-> parse(cat(p[1], p[-1])))(""||(ithprime(n))):
seq(a(n), n=1..92);  # Alois P. Heinz, Nov 23 2023

cifd[n_]:=Module[{il=IntegerLength[n],idn=IntegerDigits[n]},Which[ il==1, 10n+n, il==2,n,il>2,FromDigits[Join[{First[idn],Last[idn]}]]]]; cifd/@ Prime[ Range[70]] (* Harvey P. Dale, May 15 2012 *)

a(n) = my(d=digits(prime(n))); fromdigits(concat(d[1], d[#d])); \\ Michel Marcus, Mar 23 2018

A138841 Concatenation of initial and final digit of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 31, 17, 81, 11, 57, 27, 21, 61, 17, 17, 61, 57, 17, 17, 41, 21, 11, 27, 41, 31, 21, 41, 41, 41, 81, 57, 57, 51, 77, 17, 11, 47, 81, 61, 11, 41, 91, 17, 27, 17, 31, 11, 27, 11, 31

Offset: 1

Omar E. Pol, Apr 01 2008

			a(5)=81 because the 5th Mersenne prime is 8191, A000668(5)=8191.

Cf. A000668, A073729, A080172, A135613, A138840, A138842, A138843.

a(n) = A073729(A000668(n)). - Michel Marcus, Apr 17 2018

a(40)-a(47) from Ivan Panchenko, Apr 17 2018

A138842 Concatenation of initial and final digits of n-th even superperfect number A061652(n).

Original entry on oeis.org

22, 44, 16, 64, 46, 66, 24, 14, 16, 36, 84, 84, 36, 24, 54, 74, 26, 16, 96, 14, 26, 16, 16, 26, 26, 26, 46, 24, 24, 26, 34, 84, 66, 24, 46, 36, 66, 26, 46, 64, 14, 64, 16, 66, 14, 86, 16

Offset: 1

Omar E. Pol, Apr 02 2008

Also, concatenation of initial and final digits of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Also, concatenation of A138124(n) and A138125(n).

Cf. A019279, A061652, A073729, A138124, A138125, A138838, A138840, A138841, A138843, A138844.

More terms from Jinyuan Wang, Mar 14 2020

A138844 Concatenation of initial and final digits of n-th positive Fibonacci number.

Original entry on oeis.org

11, 11, 22, 33, 55, 88, 13, 21, 34, 55, 89, 14, 23, 37, 60, 97, 17, 24, 41, 65, 16, 11, 27, 48, 75, 13, 18, 31, 59, 80, 19, 29, 38, 57, 95, 12, 27, 39, 66, 15, 11, 26, 47, 73, 10, 13, 23, 46, 79, 15, 24, 39, 53, 82, 15, 27, 32, 59, 91, 10, 21, 41, 62, 13, 15, 28, 43, 71, 14

Offset: 1

Omar E. Pol, Apr 02 2008

Also, concatenation of A008963(n) and A003893(n).

			a(15) = 60 because the 15th positive Fibonacci number is 610 and the concatenation of initial and final digits of 610 is 60.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index entries for sequences related to Benford's law

Cf. A000045, A003893, A008963, A073729, A138840, A138841, A138842, A138843.

a:= n-> (f-> parse(cat(f[1], f[-1])))(""||(combinat[fibonacci](n))):
seq(a(n), n=1..92);  # Alois P. Heinz, Nov 23 2023

FromDigits[Join[{IntegerDigits[#][[1]]},{IntegerDigits[#][[-1]]}]]&/@ Fibonacci[Range[70]] (* Harvey P. Dale, Jun 15 2018 *)

A073730 Concatenation of largest and smallest digits of n in decimal representation.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 10, 11, 21, 31, 41, 51, 61, 71, 81, 91, 20, 21, 22, 32, 42, 52, 62, 72, 82, 92, 30, 31, 32, 33, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 44, 54, 64, 74, 84, 94, 50, 51, 52, 53, 54, 55, 65, 75, 85, 95, 60, 61, 62, 63, 64, 65, 66, 76, 86, 96

Offset: 1

Reinhard Zumkeller, Aug 05 2002

10 <= a(n) <= 99; a(a(n))=a(n).

			a(12321)=31; a(3210123)=30; a(59387)=83; a(8923)=92.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A073729.

a073730 n = 10 * a054055 n + a054054 n
-- Reinhard Zumkeller, Jul 21 2013

Table[FromDigits[{Max[x = IntegerDigits[n]], Min[x]}], {n, 69}] (* Jayanta Basu, Jul 08 2013 *)

a(n) = A054055(n)*10 + A054054(n).

A138838 Concatenation of initial and final digits of n-th even superperfect number A061652(n), divided by 2.

Original entry on oeis.org

11, 22, 8, 32, 23, 33, 12, 7, 8, 18, 42, 42, 18, 12, 27, 37, 13, 8, 48, 7, 13, 8, 8, 13, 13, 13, 23, 12, 12, 13, 17, 42, 33, 12, 23, 18, 33, 13, 23, 32, 7, 32, 8, 33, 7, 43, 8

Offset: 1

Omar E. Pol, Apr 02 2008

Also, concatenation of initial and final digits of n-th superperfect number A019279(n), divided by 2, if there are no odd superperfect numbers.

Also, concatenation of A138124(n) and A138125(n), divided by 2.

			a(5)=23 because the 5th even superperfect number A061652(5) is 4096 and the concatenation of initial and final digits of 4096 is 46 and 46/2 = 23.

Cf. A019279, A061652, A073729, A138124, A138125, A138842.

a(n) = A138842(n)/2. - Jinyuan Wang, Mar 14 2020

More terms from Jinyuan Wang, Mar 14 2020

A306689 Integers m with decimal expansion m = abc...z such that m is a multiple of both az and za; z may not be zero.

Original entry on oeis.org

11, 22, 33, 44, 55, 66, 77, 88, 99, 121, 242, 363, 484, 1001, 1092, 1111, 1207, 1221, 1275, 1331, 1441, 1458, 1512, 1551, 1661, 1729, 1771, 1785, 1881, 1932, 1991, 2002, 2112, 2184, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992, 3003, 3276, 3333, 3663, 3993, 4004, 4032

Offset: 1

Reiner Moewald, Mar 05 2019

Every power of 11 is a term. - N. J. A. Sloane, Jul 14 2019

			1512 is in the list since 12*126=1512 and 21*72=1512.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A073729.

for a in range(1,1000):
   for b in range (1, 10):
      numb = 10*a + b
      f = int(str(numb)[0])
      first = 10*f + b
      last = 10*b + f
      if numb %  first == 0 and numb % last == 0 :
         print(numb, end=', ')

A138839 Concatenation of initial and final digits of n-th perfect number, divided by 2.

Original entry on oeis.org

33, 14, 23, 44, 18, 43, 9, 14, 13, 8, 9, 9, 13, 9, 29, 9, 48, 18, 8, 24, 8, 28, 18, 48, 8, 43, 18, 9, 9, 8, 14, 9, 43, 44, 18, 8, 43, 48, 23

Offset: 1

Omar E. Pol, Apr 02 2008

Also, concatenation of A135617(n) and A094540(n), divided by 2.

			a(5)=18 because the 5th perfect number A000396(5) is 33550336 and the concatenation of initial and final digits of 33550336 is 36 and 36/2 = 18.

Cf. A000396, A073729, A135617, A094540, A138843.

cp's OEIS Frontend

A073731 Least k such that A073729(k) = n.

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A138843 Concatenation of initial and final digits of n-th perfect number.

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A138840 Concatenation of initial and final digits of n-th prime.

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A138841 Concatenation of initial and final digit of n-th Mersenne prime A000668(n).

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A138842 Concatenation of initial and final digits of n-th even superperfect number A061652(n).

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A138844 Concatenation of initial and final digits of n-th positive Fibonacci number.

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A073730 Concatenation of largest and smallest digits of n in decimal representation.

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A138838 Concatenation of initial and final digits of n-th even superperfect number A061652(n), divided by 2.

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A306689 Integers m with decimal expansion m = abc...z such that m is a multiple of both az and za; z may not be zero.

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