A138841 -id:A138841 - cp's OEIS frontend

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

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

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

A138866 Concatenation of first 3 digits and last 3 digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 3131, 127127, 819191, 131071, 524287, 214647, 230951, 618111, 162127, 170727, 686151, 531127, 104087, 147007, 446351, 259071, 190991, 285607, 478111, 346551, 281191, 431471, 448751, 402511, 854671, 536207, 521007, 512311, 746447, 174887, 129591, 412527, 814711, 623151, 127271, 437791, 924071, 125047, 299407, 122247, 315871, 124871, 202927, 169751, 316511

Offset: 1

Omar E. Pol, Apr 02 2008

L. C. Noll, Mersenne Prime Digits and Names.

Cf. A000668, A080173, A104511, A138816, A138817, A138840, A138841.

Join[{33,77,3131},FromDigits[Flatten[Join[{Take[IntegerDigits[#],3],Take[ IntegerDigits[ #],-3]}]]]&/@ (2^MersennePrimeExponent[Range[4,40]]-1)] (* Harvey P. Dale, Dec 30 2023 *)

More terms from Harvey P. Dale, Dec 30 2023

A138818 Concatenation of initial digit of n-th even superperfect number A061652(n), initial digit of n-th Mersenne prime A000668(n) and initial digit of n-th perfect number A000396(n).

Original entry on oeis.org

236, 472, 134, 618, 483, 618, 251, 122, 122, 361, 811, 811

Offset: 1

Omar E. Pol, Apr 05 2008

Also, concatenation of initial digit of n-th superperfect number A019279(n), initial digit of n-th Mersenne prime A000668(n) and initial digit of n-th perfect number A000396(n), if there are no odd superperfect numbers.

Also, concatenation of A138124(n), A135613(n) and A135617(n).

L. C. Noll, Mersenne Prime Digits and Names.
J. M. Pedersen, Known Perfect Numbers.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000396, A000668, A019279, A061652, A135613, A135617, A138124, A138816, A138817, A138819, A138841, A138842, A138843.

A138819 Concatenation of final digit of n-th even superperfect number A061652(n), final digit of n-th Mersenne prime A000668(n) and final digit of n-th perfect number A000396(n).

Original entry on oeis.org

236, 478, 616, 478, 616, 616, 478, 478, 616, 616, 478, 478, 616, 478, 478, 478, 616, 616, 616, 478, 616, 616, 616, 616, 616, 616, 616, 478, 478, 616, 478, 478, 616, 478, 616, 616, 616, 616, 616

Offset: 1

Omar E. Pol, Apr 05 2008

Also, concatenation of final digit of n-th superperfect number A019279(n), final digit of n-th Mersenne prime A000668(n) and final digit of n-th perfect number A000396(n), if there are no odd superperfect numbers.
Also, concatenation of A138125(n), A080172(n) and A094540(n).
For n>1 a(n) is equal to 478 or 616, only.
Note that, for n>1: if the final digit of n-th Mersenne prime A000668(n) is 1 then the final digit of n-th even superperfect number is 6 and the final digit of n-th perfect number also is 6, otherwise the final digit of n-th even superperfect number is 4 and the final digit of n-th perfect number is 8 (see example).

			===================================================================
.................. SHORT TABLE OF FINAL DIGITS ...................
===================================================================
... Final digit of even ..... Final digit of ..... Final digit of
... superperfect number ..... Mersenne prime ..... perfect number
........ A061652 ............... A000668 ............. A000396
===================================================================
n = 1 ..... (2) ................... (3) .................. (6)
n > 1 ..... (4) ................... (7) .................. (8)
n > 1 ..... (6) ................... (1) .................. (6)

L. C. Noll, Mersenne Prime Digits and Names.
J. M. Pedersen, Known Perfect Numbers.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000396, A000668, A019279, A061652, A080172, A094540, A138125, A138816, A138817, A138818, A138841, A138842, A138843.

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 *)

A138863 Concatenation of first two digits and last two digits of n-th Mersenne prime A000668(n).

Original entry on oeis.org

33, 77, 3131, 1227, 8191, 1371, 5287, 2147, 2351, 6111, 1627, 1727, 6851, 5327, 1087, 1407, 4451, 2571, 1991, 2807, 4711, 3451, 2891, 4371, 4451, 4011, 8571, 5307, 5207, 5111, 7447, 1787, 1291, 4127, 8111, 6251, 1271, 4391, 9271, 1247, 2907, 1247, 3171, 1271, 2027, 1651, 3111

Offset: 1

Omar E. Pol, Apr 02 2008

L. C. Noll, Mersenne Prime Digits.

Cf. A000668, A080173, A104511, A138816, A138817, A138840, A138841, A138862, A138864, A138865, A138866.

More terms from Jinyuan Wang, Mar 14 2020

cp's OEIS Frontend

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

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A138866 Concatenation of first 3 digits and last 3 digits of n-th Mersenne prime A000668(n).

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A138818 Concatenation of initial digit of n-th even superperfect number A061652(n), initial digit of n-th Mersenne prime A000668(n) and initial digit of n-th perfect number A000396(n).

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A138819 Concatenation of final digit of n-th even superperfect number A061652(n), final digit of n-th Mersenne prime A000668(n) and final digit of n-th perfect number A000396(n).

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

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A138863 Concatenation of first two digits and last two digits of n-th Mersenne prime A000668(n).

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