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 A062786 Centered 10-gonal numbers. 28
 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901, 2101, 2311, 2531, 2761, 3001, 3251, 3511, 3781, 4061, 4351, 4651, 4961, 5281, 5611, 5951, 6301, 6661, 7031, 7411, 7801, 8201, 8611, 9031, 9461, 9901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Deleting the least significant digit yields the (n-1)-st triangular number: a(n) = 10*A000217(n-1) +1. - Amarnath Murthy, Dec 11 2003 All divisors of a(n) are congruent to 1 or -1, modulo 10; that is, they end in the decimal digit 1 or 9. Proof: If p is an odd prime different from 5 then 5n^2 - 5n + 1 = 0 (mod p) implies 25(2n - 1)^2 = 5 (mod p), whence p = 1 or -1 (mod 10). - Nick Hobson, Nov 13 2006 Centered decagonal numbers. - Omar E. Pol, Oct 03 2011 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1) FORMULA a(n) = 5n(n-1) + 1. Binomial transform of [1, 10, 10, 0, 0, 0,...]; Narayana transform (A001263) of [1, 10, 0, 0, 0,...]. - Gary W. Adamson, Dec 29 2007 a(n) = 10*n + a(n-1) - 10 (with a(1)=1). - Vincenzo Librandi, Aug 07 2010 G.f. -x*(1+8*x+x^2) / (x-1)^3. - R. J. Mathar, Feb 04 2011 a(n) = A124080(n-1) + 1. - Omar E. Pol, Oct 03 2011 a(n) = A101321(10,n-1). - R. J. Mathar, Jul 28 2016 MATHEMATICA lst={}; Do[p=(5*(n^2-n))+1; AppendTo[lst, p], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *) FoldList[#1 + #2 &, 1, 10 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *) PROG (PARI) j=[]; for(n=1, 75, j=concat(j, (5*n*(n-1)+1))); j (PARI) for (n=1, 1000, write("b062786.txt", n, " ", 5*n*(n - 1) + 1) ) \\ Harry J. Smith, Aug 11 2009 CROSSREFS Cf. A001263. Sequence in context: A113747 A202007 A125239 * A090562 A174244 A136061 Adjacent sequences:  A062783 A062784 A062785 * A062787 A062788 A062789 KEYWORD easy,nonn AUTHOR Jason Earls, Jul 19 2001 EXTENSIONS Better description from Terrel Trotter, Jr., Apr 06 2002 STATUS approved

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Last modified November 19 04:53 EST 2018. Contains 317333 sequences. (Running on oeis4.)