A135613 -id:A135613 - cp's OEIS frontend

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

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

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

A296442 Initial digit of n-th Mersenne number.

Original entry on oeis.org

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

Offset: 1

Michel Marcus, Dec 13 2017

			The 4th Mersenne number is 127, so a(4) = 1.

Robert Israel, Table of n, a(n) for n = 1..10000
Zhaodong Cai, Matthew Faust, A.J. Hildebrand, Junxian Li, Yuan Zhang, Leading Digits of Mersenne Numbers, arXiv:1712.04425 [math.NT], 2017.

Cf. A000030, A001348.

A135613, for Mersenne primes, is a subsequence.

initialdig:= n -> floor(n/10^ilog10(n)):
seq(initialdig(2^ithprime(i)-1),i=1..100); # Robert Israel, Dec 13 2017

Array[First@ IntegerDigits[2^Prime[#] - 1] &, 105] (* Michael De Vlieger, Dec 13 2017 *)

PARI
```
a(n) = digits(2^prime(n)-1)[1];
```

a(n) = A000030(A001348(n)).

cp's OEIS Frontend

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

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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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A296442 Initial digit of n-th Mersenne number.

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