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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). 5

%I #9 Mar 11 2014 01:34:11

%S 236,478,616,478,616,616,478,478,616,616,478,478,616,478,478,478,616,

%T 616,616,478,616,616,616,616,616,616,616,478,478,616,478,478,616,478,

%U 616,616,616,616,616

%N 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).

%C 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.

%C Also, concatenation of A138125(n), A080172(n) and A094540(n).

%C For n>1 a(n) is equal to 478 or 616, only.

%C 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).

%H L. C. Noll, <a href="http://isthe.com/chongo/tech/math/prime/mersenne.html">Mersenne Prime Digits and Names</a>.

%H J. M. Pedersen, <a href="http://amicable.homepage.dk/perfect.htm">Known Perfect Numbers</a>.

%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%e ===================================================================

%e .................. SHORT TABLE OF FINAL DIGITS ...................

%e ===================================================================

%e ... Final digit of even ..... Final digit of ..... Final digit of

%e ... superperfect number ..... Mersenne prime ..... perfect number

%e ........ A061652 ............... A000668 ............. A000396

%e ===================================================================

%e n = 1 ..... (2) ................... (3) .................. (6)

%e n > 1 ..... (4) ................... (7) .................. (8)

%e n > 1 ..... (6) ................... (1) .................. (6)

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

%K base,nonn,less

%O 1,1

%A _Omar E. Pol_, Apr 05 2008

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)