A098739 This sequence is constructed using only the four single-digit primes 2,3,5,7 in that order.

2, 23, 235, 2357, 23572, 235723, 2357235, 23572357, 235723572, 2357235723, 23572357235, 235723572357, 2357235723572, 23572357235723, 235723572357235, 2357235723572357, 23572357235723572, 235723572357235723, 2357235723572357235, 23572357235723572357, 235723572357235723572

Offset

1,1

Comments

The idea for the sequence came from the way long DNA sequences are produced from only four bases, namely, A,T,G,C. Nature is able to produce remarkable species on Earth by permuting these four bases in an apparent random order. The connection between the arrangement of DNA bases in the chromosomes of species and the number system is poorly understood.

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (10,0,0,1,-10).

Formula

G.f.: x*(2 + 3*x + 5*x^2 + 7*x^3) / ( (x-1)*(10*x-1)*(1+x)*(1+x^2) ). - R. J. Mathar, Feb 03 2011

E.g.f.: (3366*cos(x) - 8080*cosh(x) + 4714*cosh(10*x) + 3663*sin(x) - 10807*sinh(x) + 4714*sinh(10*x))/19998. - Stefano Spezia, Aug 11 2025

Mathematica

CoefficientList[Series[x (2+3x+5x^2+7x^3)/((x-1)(10x-1) (1+x)(1+x^2)), {x, 0, 50}], x]  (* Harvey P. Dale, Mar 20 2011 *)

Crossrefs

Cf. A019518.

Sequence in context: A294268 A118385 A386964 * A287353 A091762 A309706

Adjacent sequences: A098736 A098737 A098738 * A098740 A098741 A098742

Keyword

nonn,base,easy

Author

Parthasarathy Nambi, Sep 30 2004

Extensions

a(11)-a(21) from Stefano Spezia, Aug 11 2025

Status

approved