A038508 -id:A038508 - cp's OEIS frontend

A094297 Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 2, s(n) = 2.

1, 3, 7, 18, 46, 120, 316, 840, 2248, 6048, 16336, 44256, 120160, 326784, 889792, 2424960, 6613120, 18043392, 49247488, 134450688, 367134208, 1002645504, 2738510848, 7480215552, 20433258496, 55818559488, 152486858752

Offset: 1

Herbert Kociemba, Jun 02 2004

In general, a(n,m,j,k) = (2/m)*Sum_{r=1..m-1) sin(j*r*Pi/m)*sin(k*r*Pi/m)*(1+2*cos(Pi*r/m))^n is the number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < m and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = j, s(n) = k.

Robert Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (4,-2,-4).

First differences of A038508.

a(n) = (1/3)*Sum_{k=1..5} sin(Pi*k/3)^2*(1+2*cos(Pi*k/6))^n or a(n) = (2^n + (1-sqrt(3))^n + (1 + sqrt(3))^n)/4.
(a(n)) seems to be given by tesseq(- 2'i + 2'j + 2'k - 2i' + 2j' + 2k' - 2'ii' + 2'jj' - 'kk' - 2.5'ik' - 1.5'jk' - 2.5'ki' - 1.5'kj' - e) (disregarding signs) - Creighton Dement, Nov 17 2004
G.f.: ( 1-x-3*x^2 )*x / ( (2*x-1)*(2*x^2+2*x-1) ). - R. J. Mathar, Sep 11 2019
4*a(n) = 2^n + 2*A026150(n). - R. J. Mathar, Oct 25 2022

A162252 Numbers of the form prime(prime(prime(k))) with a digit sum which is prime.

Original entry on oeis.org

5, 11, 179, 331, 599, 919, 1297, 1523, 1787, 2221, 3259, 3637, 3943, 4397, 5381, 6113, 6661, 6823, 8221, 9859, 10631, 11953, 12097, 12301, 12547, 12763, 13469, 14723, 15641, 15823, 17627, 18149, 19577, 20063, 20773, 21529, 23431, 26371, 26489

Offset: 1

Cino Hilliard, Jun 28 2009

Members of A038580 with a digit sum which is prime.

			For k=6, prime(prime(prime(6))) = A038580(6)=179. The digit sum 1+7+9 = 17 is prime, so 179 is in the sequence.

read("transforms") ; A038580 := proc(n) ithprime(ithprime(ithprime(n))) ; end:
for n from 1 to 80 do if isprime(digsum(A038580(n))) then printf("%d,", A038580(n)) ; fi; od: # R. J. Mathar, Aug 14 2009

Select[Table[Nest[Prime, x, 3], {x, 1, 100}],
PrimeQ[Total[IntegerDigits[#, 10]]] &]

sodip2(n,m) = /* m multiple nesting of prime(prime(prime..(n) */
{ local(s=0,a,x,y,j,p);
for(x=1,n, p=prime(x);
for(i=1,m,p=prime(p));
a=eval(Vec(Str(p))); y=sum(j=1,length(a),a[j]); if(isprime(y),print1(p","));)
}

{A038508(k): A007953(A038508(k)) in A000040, any k}.

Edited by R. J. Mathar, Aug 14 2009

cp's OEIS Frontend

A094297 Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 2, s(n) = 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A162252 Numbers of the form prime(prime(prime(k))) with a digit sum which is prime.

Views

Author

Keywords

Comments

Examples

Programs

Maple

Mathematica

PARI

Formula

Extensions