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A007907 Concatenation of sequence (1,2,..,[(n-1)/2],[n/2],[n/2]-1,..,1) for n >= 1. 5
1, 11, 121, 1221, 12321, 123321, 1234321, 12344321, 123454321, 1234554321, 12345654321, 123456654321, 1234567654321, 12345677654321, 123456787654321, 1234567887654321, 12345678987654321 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also called Smarandache symmetric numbers.

For n < 4900, a(2) = A259937(1) = 11, a(19) = A173426(10) = 12345678910987654321, a(20) = A259937(10) = 1234567891010987654321 and a(4891) = A173426(2446) = 1234567..244524462445..7654321 are primes (see A173426 and A259937). - XU Pingya, May 19 2017

REFERENCES

M. Le, The Primes in the Smarandache Symmetric Sequences, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 174-175.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..405 [The list of terms has an interesting visual appearance]

F. Smarandache, Only Problems, Not Solutions!

Eric Weisstein's World of Mathematics, Smarandache Sequences

FORMULA

a(n)=a1+a2+a3, where a1=floor{a(n-1)/[10^(k+y*w)]}*10^(k+w+y*k2) a2=(w2*y2+b*y)*10^(k+y*w) a3=a(n-1)-floor{a(n-1)/[10^(k+y*w)]}*10^(k+y*w) being k=floor{(floor[1+log10(a(n-1)))-x*w]/2} k2=floor[1+log10(b)] x=[3+(-1)^(n+1)]/2 y=[1+(-1)^(n+1)]/2 y2=[1+(-1)^n]/2 b=[2*n+1+(-1)^(n+1)]/4 w=floor{1+log10[(2*(n-1)+1+(-1)^n)/4]} w2=[2*(n-1)+1+(-1)^n]/4. - Paolo P. Lava, Jun 04 2008

MAPLE

P:=proc(n) local a, a1, a2, a3, b, k, k2, i, w, w2, x, y, y2; a:=1; print(a); for i from 2 by 1 to n do x:=(3+(-1)^(i+1))/2; y:=(1+(-1)^(i+1))/2; y2:=(1+(-1)^i)/2; b:=(2*i+1+(-1)^(i+1))/4; w:=floor(evalf(1+log10((2*(i-1)+1+(-1)^i)/4), 1000)); w2:=(2*(i-1)+1+(-1)^i)/4; k:=floor((floor(evalf(1+log10(a), 1000))-(x)*w)/2); k2:=floor(evalf(1+log10(b), 1000)); a1:=floor(evalf(a/(10^(k+y*w)), 1000))*10^(k+w+y*k2); a2:=(w2*y2+b*y)*10^(k+y*w); a3:=a-floor(evalf(a/10^(k+y*w), 1000))*10^(k+y*w); a:=a1+a2+a3; print(a); od; end: P(500); # Paolo P. Lava, Jun 04 2008

MATHEMATICA

Table[FromDigits@ Flatten@ Map[IntegerDigits, Apply[Join, {#, If[OddQ@ n, Rest@ #, #] &@ Reverse@ #}]] &@ Range@ Ceiling[n/2]], {n, 17}]

CROSSREFS

Sequence in context: A125315 A223676 A132583 * A171285 A216132 A088113

Adjacent sequences:  A007904 A007905 A007906 * A007908 A007909 A007910

KEYWORD

nonn,base,changed

AUTHOR

R. Muller

STATUS

approved

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Last modified May 28 21:38 EDT 2017. Contains 287241 sequences.