A079360 -id:A079360 - cp's OEIS frontend

A143095 (1, 2, 4, 8, ...) interleaved with (4, 8, 16, 32, ...).

1, 4, 2, 8, 4, 16, 8, 32, 16, 64, 32, 128, 64, 256, 128, 512, 256, 1024, 512, 2048, 1024, 4096, 2048, 8192, 4096, 16384, 8192, 32768, 16384, 65536, 32768, 131072, 65536, 262144, 131072, 524288, 262144, 1048576, 524288, 2097152, 1048576, 4194304

Offset: 0

Gary W. Adamson & Roger L. Bagula, Jul 23 2008

Partial sums are in A079360. a(n) = A076736(n+5). - Klaus Brockhaus, Jul 27 2009

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2).

Cf. A048655.

seq(coeff(series((1+4*x)/(1-2*x^2), x, n+1), x, n), n = 0..45); # G. C. Greubel, Mar 13 2020

nn=30;With[{p=2^Range[0,nn]},Riffle[Take[p,nn-2],Drop[p,2]]] (* Harvey P. Dale, Oct 03 2011 *)

A143095(n):=(5-3*(-1)^n)*2^(1/4*(2*n-1+(-1)^n))/2$
makelist(A143095(n),n,0,30); /* Martin Ettl, Nov 03 2012 */

for(n=0, 41, print1((5-3*(-1)^n)*2^(1/4*(2*n-1+(-1)^n))/2, ",")) \\ Klaus Brockhaus, Jul 27 2009

[(5 -3*(-1)^n)*2^((2*n-1+(-1)^n)/4)/2 for n in (0..45)] # G. C. Greubel, Mar 13 2020

Inverse binomial transform of A048655: (1, 5, 11, 27, 65, 157, ...).
a(n) = A135530(n+1). - R. J. Mathar, Aug 02 2008
From Klaus Brockhaus, Jul 27 2009: (Start)
a(n) = (5 - 3*(-1)^n) * 2^((2*n-1+(-1)^n)/4)/2.
a(n) = 2*a(n-2) for n > 1; a(0) = 1, a(1) = 4.
G.f.: (1+4*x)/(1-2*x^2). (End)
a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

More terms from Klaus Brockhaus, Jul 27 2009

A079361 Primes in the sequence of sums of alternating powers of 2.

Original entry on oeis.org

5, 7, 19, 43, 379, 1531, 3067, 24571, 98299, 100663291, 6442450939, 51539607547, 844424930131963, 13510798882111483, 55340232221128654843, 1947111321950560360698936123457531, 133804471191183738849214309635890169035882491

Offset: 1

Cino Hilliard, Feb 15 2003

nonn

Sum of reciprocals = 0.4224131591021966740339033736...

Primes in A079360. - R. J. Mathar, Dec 03 2014

Amiram Eldar, Table of n, a(n) for n = 1..29

Cf. A079360.

/* Primes in the sequence of sums of alternating powers of 2 */ pseq(n) = { j=a=1; p=2; sr=0; while(j<=n, a = a + 2^(p); if(isprime(a),print1(a" "); sr+=1.0/a; ); a = a+2^(p-1); if(isprime(a),print1(a" "); sr+=1.0/a; ); p+=1; j+=2; ); print(); print(sr); }

Offset changed by Georg Fischer, Sep 02 2022

a(16)-a(17) from Amiram Eldar, Jul 06 2024

A079362 Sequence of sums of alternating powers of 3.

Original entry on oeis.org

1, 4, 5, 14, 17, 44, 53, 134, 161, 404, 485, 1214, 1457, 3644, 4373, 10934, 13121, 32804, 39365, 98414, 118097, 295244, 354293, 885734, 1062881, 2657204, 3188645, 7971614, 9565937, 23914844, 28697813, 71744534, 86093441, 215233604

Offset: 1

Cino Hilliard, Feb 15 2003

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,-3).

Cf. A079360, A079363, A028242, A048473 (bisection).

a:=[1,4,5];; for n in [4..30] do a[n]:=a[n-1]+3*a[n-2]-3*a[n-3]; od; a; # G. C. Greubel, Aug 07 2019

I:=[1,4,5]; [n le 3 select I[n] else Self(n-1) +3*Self(n-2) -3*Self(n-3): n in [1..40]]; // G. C. Greubel, Aug 07 2019

a[1]:=1:a[2]:=4:for n from 3 to 100 do a[n]:=3*a[n-2]+2 od: seq(a[n], n=1..33); # Zerinvary Lajos, Mar 17 2008

LinearRecurrence[{1,3,-3},{1,4,5},40] (* Harvey P. Dale, Oct 18 2016 *)

a(n)=if(n<1,0,1+sum(k=2,n,3^((k\2)-(k%2))))

a(n)=if(n<0,0,(5/3-3*n%2)*2^ceil(n/2)-1)

@CachedFunction
def a(n):
    if (n==0): return 1
    elif (1<=n<=2): return n+3
    else: return a(n-1) + 3*a(n-2) - 3*a(n-3)
[a(n) for n in (0..40)] # G. C. Greubel, Aug 07 2019

G.f.: x*(1+3*x-2*x^2)/((1-x)*(1-3*x^2)). - Michael Somos, Feb 18 2003

For n >= 1, a(2n-1) = (2/3)*3^n - 1, a(2n) = (5/3)*3^n - 1. - Benoit Cloitre, Feb 16 2003

cp's OEIS Frontend

A143095 (1, 2, 4, 8, ...) interleaved with (4, 8, 16, 32, ...).

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A079361 Primes in the sequence of sums of alternating powers of 2.

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PARI

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A079362 Sequence of sums of alternating powers of 3.

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GAP

Magma

Maple

Mathematica

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PARI

Sage

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