A138818 -id:A138818 - cp's OEIS frontend

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).

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.

A138820 Concatenation of n-th even superperfect number, n-th Mersenne prime A000668(n) and n-th perfect number.

Original entry on oeis.org

236, 4728, 1631496, 641278128, 4096819133550336, 655361310718589869056, 262144524287137438691328, 107374182421474836472305843008139952128, 115292150460684697623058430092136939512658455991569831744654692615953842176

Offset: 1

Omar E. Pol, Apr 05 2008

Concatenation of A061652(n), A000668(n) and A000396(n).

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

Cf. A000396, A000668, A019279, A061652, A138818, A138819.

A138833 Concatenation of n-th perfect number and n-th Mersenne prime A000668(n).

Original entry on oeis.org

63, 287, 49631, 8128127, 335503368191, 8589869056131071, 137438691328524287, 23058430081399521282147483647, 26584559915698317446546926159538421762305843009213693951, 191561942608236107294793378084303638130997321548169216618970019642690137449562111

Offset: 1

Omar E. Pol, Apr 06 2008

a(15) has 1156 digits. - Harvey P. Dale, Jan 10 2023

			a(3)=49631 because A000396(3)=496 and A000668(3)=31.

Harvey P. Dale, Table of n, a(n) for n = 1..14

Cf. A000396, A000668, A138816, A138817, A138818, A138819, A138820, A138821, A138822, A138832.

Module[{nn=10},FromDigits[Flatten[IntegerDigits/@#]]&/@Thread[{PerfectNumber[ Range[ nn]],2^ MersennePrimeExponent[ Range[nn]]-1}]] (* Harvey P. Dale, Jan 10 2023 *)

Corrected and extended by Harvey P. Dale, Jan 10 2023

A138832 Concatenation of n-th Mersenne prime A000668(n) and n-th perfect number.

Original entry on oeis.org

36, 728, 31496, 1278128, 819133550336, 1310718589869056, 524287137438691328, 21474836472305843008139952128, 23058430092136939512658455991569831744654692615953842176

Offset: 1

Omar E. Pol, Apr 06 2008

			a(3)=31496 because A000668(3)=31 and A000396(3)=496.

Cf. A000396, A000668, A138816, A138817, A138818, A138819, A138820, A138821, A138822, A138833.

A138728 Array read by rows: row n lists n-th even superperfect number A061652(n), n-th Mersenne prime A000668(n) and n-th perfect number A000396(n).

Original entry on oeis.org

2, 3, 6, 4, 7, 28, 16, 31, 496, 64, 127, 8128, 4096, 8191, 33550336, 65536, 131071, 8589869056, 262144, 524287, 137438691328, 1073741824, 2147483647, 2305843008139952128, 1152921504606846976, 2305843009213693951

Offset: 1

Omar E. Pol, Apr 07 2008

			Array begins:
2, 3, 6
4, 7, 28
16, 31, 496

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, A138818, A138819.

cp's OEIS Frontend

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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A138820 Concatenation of n-th even superperfect number, n-th Mersenne prime A000668(n) and n-th perfect number.

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A138833 Concatenation of n-th perfect number and n-th Mersenne prime A000668(n).

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A138832 Concatenation of n-th Mersenne prime A000668(n) and n-th perfect number.

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A138728 Array read by rows: row n lists n-th even superperfect number A061652(n), n-th Mersenne prime A000668(n) and n-th perfect number A000396(n).

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