A135617 -id:A135617 - 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.

A138125 Final digit of n-th even superperfect number A061652(n).

Original entry on oeis.org

2, 4, 6, 4, 6, 6, 4, 4, 6, 6, 4, 4, 6, 4, 4, 4, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 4, 4, 6, 4, 6, 6, 6, 6, 6, 4, 4, 4, 6, 6, 4, 6, 6

Offset: 1

Omar E. Pol, Apr 01 2008, corrected Apr 03 2008

Also, final digit of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

			a(5)=6 because the 5th even superperfect number A061652(5) is 4096 and the final digit of 4096 is 6.
a(34)=4 because the final digit of 34th Mersenne prime is 7. a(39)=6 because the final digit of 39th Mersenne prime is 1.
.............................................................
............... SHORT TABLE OF FINAL DIGITS .................
.............................................................
Final digit of ..... Final digit of Even ..... Final digit of
Mersenne prime ..... Superperfect number ..... Perfect number
A000668 ............ A061652 ................. A000396........
(3) ................ (2) ..................... (6) ........... (For n=1, only)
(7) ................ (4) ..................... (8) ...........
(1) ................ (6) ..................... (6) ...........

Landon Curt Noll, Mersenne Prime Digits.

Cf. A000030, A000396, A000668, A077648, A019279, A061652, A135613, A135617, A138125.

Mod[#,10]&/@(2^(MersennePrimeExponent[Range[47]]-1)) (* Harvey P. Dale, Feb 23 2023 *)

a(1)=2. For n>1, if final digit of n-th Mersenne prime A000668(n) is equal to 1 then a(n)=6, otherwise a(n)=4.

a(40)-a(47) from Jinyuan Wang, Mar 14 2020

A138816 Concatenation of initial digit of n-th Mersenne prime A000668(n), initial digit of n-th even superperfect number A061652(n) and initial digit of n-th perfect number A000396(n).

Original entry on oeis.org

326, 742, 314, 168, 843, 168, 521, 212, 212, 631, 181, 181, 632, 521, 155

Offset: 1

Omar E. Pol, Apr 01 2008

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

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

L. C. Noll, Mersenne Prime Digits and Names.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000396, A000668, A019279, A061652, A135613, A135617, A138124, A138817.

a(13)-a(15) from Robert Price, Jun 16 2019

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.

A138124 Initial digit of n-th even superperfect number A061652(n).

Original entry on oeis.org

2, 4, 1, 6, 4, 6, 2, 1, 1, 3, 8, 8, 3, 2, 5, 7, 2, 1, 9, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 2, 3, 8, 6, 2, 4, 3, 6, 2, 4

Offset: 1

Omar E. Pol and Robert G. Wilson v, Apr 01 2008

Also, initial digit of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

			a(5)=4 because the 5th even superperfect number A061652(5) is 4096 and the initial digit of 4096 is 4.

Cf. A000030, A077648, A019279, A061652, A135613, A135617, A138125.

lst = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917}; f[n_] := Block[{pn = 2^(n - 1)}, Quotient[pn, 10^Floor[Log[10, pn]]]]; f@# & /@ (* Robert G. Wilson v, Apr 01 2008 *)

a(13)-a(39) from Robert G. Wilson v, Apr 01 2008

A138876 First 3 digits of n-th even perfect number.

Original entry on oeis.org

6, 28, 496, 812, 335, 858, 137, 230, 265, 191, 131, 144, 235, 141, 541, 108, 994, 335, 182, 407, 114, 598, 395, 931, 100, 811, 365, 144, 136, 131, 278, 151, 838, 849, 331, 194, 811, 955, 427, 793, 448, 746, 497, 775, 204, 144, 500

Offset: 1

Omar E. Pol, Apr 02 2008

As of August 6, 2018, GIMPS reports that all Mersenne primes through the 47th have been positively identified, i.e., that there are no further such primes below the 47th. Thus, the sequence through a(47), i.e., through the term 500, is complete. Additional terms (169, 451, 109) are correct but it is still possible that more terms may be found above a(47) but below a(50). [Harvey P. Dale, Jul 17 2011] [Updated by Ivan Panchenko, Aug 06 2018]

Jan Munch Pedersen, Known Perfect Numbers [From Steven Bi (chenhsi(AT)stanford.edu), Jan 18 2009] [Replaced with Wayback Machine link by _Felix Fröhlich_, Aug 04 2018]
Omar E. Pol, Los numeros perfectos

Cf. A000396, A135617, A138864, A138873, A138877.

First three digits of each term from A138877. [Steven Bi (chenhsi(AT)stanford.edu), Jan 18 2009]

f[n_] := Block[{e, p, mpe = MersennePrimeExponent@ n}, p = (2^mpe - 1) 2^(mpe - 1); e = IntegerLength@ p - 3; If[e < 1, p, Quotient[p, 10^e]]]; Array[f, 44] (* Robert G. Wilson v, Aug 06 2018 *)

a(15)-a(31) added by Steven Bi (chenhsi(AT)stanford.edu), Jan 18 2009
Corrected a(27) and added a(32) through a(40) by Harvey P. Dale, Jul 17 2011
Definition changed (inserting the word "even") and a(41)-a(47) added by Ivan Panchenko, Aug 04 2018

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

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

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A138125 Final digit of n-th even superperfect number A061652(n).

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A138816 Concatenation of initial digit of n-th Mersenne prime A000668(n), initial digit of n-th even superperfect number A061652(n) and initial digit of n-th perfect number A000396(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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A138124 Initial digit of n-th even superperfect number A061652(n).

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A138876 First 3 digits of n-th even perfect number.

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

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