A138817 -id:A138817 - cp's OEIS frontend

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

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

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.

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.

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

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.

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

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).

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

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).

Views

Author

Keywords

Comments

Links

Crossrefs

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).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

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

Views

Author

Keywords

Links

Crossrefs

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Examples

Crossrefs