A057902 -id:A057902 - cp's OEIS frontend

A057901 a(n) = 3^prime(n).

9, 27, 243, 2187, 177147, 1594323, 129140163, 1162261467, 94143178827, 68630377364883, 617673396283947, 450283905890997363, 36472996377170786403, 328256967394537077627, 26588814358957503287787

Offset: 1

Henry Bottomley, Sep 29 2000

nonn

			a(4) = 3^7 = 2187.

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Cf. A034785, A053810, A057902, A132800.

Subsequence of A000244 (powers of 3).

[3^p: p in PrimesUpTo(30)]; // Vincenzo Librandi, Jun 03 2014

3^Prime@Range@30 (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)

a(n) = 3^A000040(n).

Sum_{n>=1} 1/a(n) = A132800. - Amiram Eldar, Aug 11 2020

A132797 Decimal expansion of Sum_{n >= 1} 1/5^prime(n).

Original entry on oeis.org

0, 4, 8, 3, 3, 2, 8, 2, 1, 3, 0, 0, 5, 6, 3, 2, 3, 2, 6, 9, 1, 6, 6, 3, 4, 7, 1, 2, 5, 1, 5, 6, 6, 5, 9, 6, 5, 2, 2, 7, 0, 2, 3, 4, 1, 0, 3, 4, 0, 1, 5, 8, 2, 7, 2, 2, 9, 4, 9, 6, 7, 7, 4, 6, 8, 3, 9, 2, 7, 9, 1, 6, 6, 9, 7, 5, 0, 9, 6, 0, 6, 5, 1, 5, 2, 7, 2, 3, 8, 6, 6, 3, 8, 6, 6, 1, 6, 0

Offset: 0

Cino Hilliard, Nov 17 2007

Equivalently, the real number in (0,1) having the characteristic function of the primes, A010051, as its base-5 expansion. - M. F. Hasler, Jul 04 2017

			0.0483328213005632326916634712515665965227023410340158272294967746839279...

Cf. A000720, A051006 (analog for base 2), A057902, A132800 (analog for base 3), A132806 (analog for base 4), A010051 (characteristic function of the primes), A132817 (base 6).

/* Sum of 1/m^p for primes p */ sumnp(n,m) = { local(s=0,a,j); for(x=1,n, s+=1./m^prime(x); ); a=Vec(Str(s)); for(j=3,n, print1(eval(a[j])",") ) }

suminf(n=1, 1/5^prime(n)) \\ Then: digits(%\.1^default(realprecision))[1..-3] to remove the last 2 digits. N.B.: Functions sumpos() and sumnum() yield much less accurate results. - M. F. Hasler, Jul 04 2017

From Amiram Eldar, Aug 11 2020: (Start)
Equals Sum_{k>=1} 1/A057902(k).
Equals 4 * Sum_{k>=1} pi(k)/5^(k+1), where pi(k) = A000720(k). (End)

Offset corrected R. J. Mathar, Jan 26 2009

Edited by M. F. Hasler, Jul 04 2017

A135175 a(n) = 5^p + 3^p - 2^p, where p = prime(n).

Original entry on oeis.org

30, 144, 3336, 80184, 49003224, 1222289256, 763068462216, 19074648065304, 11921023089868344, 186264583552936197096, 4656613490748641378424, 72759576592118027485247016, 45474735125119406073899483976, 1136868377544417255992242883544, 710542735786689000089344282510584

Offset: 1

Omar E. Pol, Nov 25 2007

			a(4)=80184 because the 4th prime number is 7, 5^7=78125, 3^7=2187, 2^7=128 and 78125+2187-128=80184.

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. 2^p: A034785. 3^p: A057901. 2^5: A057902.

[5^p+3^p-2^p: p in PrimesUpTo(100)]; // Vincenzo Librandi, Dec 14 2010

a:= n-> (p-> 5^p+3^p-2^p)(ithprime(n)):
seq(a(n), n=1..15);  # Alois P. Heinz, Jun 08 2025

5^#+3^#-2^#&/@Prime[Range[20]]  (* Harvey P. Dale, Apr 04 2011 *)
Table[5^p + 3^p - 2^p, {p, Prime[Range[20]]}] (* Vincenzo Librandi, May 24 2014 *)

a(n) = 5^p + 3^p - 2^p with p = A000040(n).

More terms from Vincenzo Librandi, Dec 14 2010

A269327 a(n) = 7^prime(n).

Original entry on oeis.org

49, 343, 16807, 823543, 1977326743, 96889010407, 232630513987207, 11398895185373143, 27368747340080916343, 3219905755813179726837607, 157775382034845806615042743, 18562115921017574302453163671207, 44567640326363195900190045974568007

Offset: 1

Emre APARI, Feb 23 2016

			The second prime is 3, hence a(2) = 7^3 = 343.
The third prime is 5, hence a(3) = 7^5 = 16807.

Cf. A000040, A000420, A034785, A053810, A057901, A057902, A132822.

[7^p: p in PrimesUpTo(45)]; // Vincenzo Librandi, Feb 25 2016

A269327:=n->7^ithprime(n): seq(A269327(n), n=1..20); # Wesley Ivan Hurt, Mar 07 2016

7^Prime[Range[20]] (* Alonso del Arte, Feb 23 2016 *)

a(n) = 7^prime(n); \\ Altug Alkan, Mar 04 2016

a(n) = 7^A000040(n).

Sum_{n>=1} 1/a(n) = A132822. - Amiram Eldar, Aug 11 2020

A135173 a(n) = 5^p - 3^p - 2^p, where p = prime(n).

Original entry on oeis.org

12, 90, 2850, 75810, 48648930, 1219100610, 762810181890, 19072323542370, 11920834803510690, 186264446292181467330, 4656612255401848810530, 72759575691550215703252290, 45474735052173413319557911170, 1136868376887903321203168728290, 710542735733511371371429275935010

Offset: 1

Omar E. Pol, Nov 25 2007

nonn

			a(4) = 75810 because the 4th prime number is 7, 5^7 = 78125, 3^7 = 2187, 2^7 = 128 and 78125-2187-128 = 75810.

Ivan Panchenko, Table of n, a(n) for n = 1..200

Cf. A034785 (2^p), A057901 (3^p), A057902 (5^p).

[5^p-3^p-2^p: p in PrimesUpTo(100)]; // Vincenzo Librandi, Dec 14 2010

a:= n-> (p-> 5^p-3^p-2^p)(ithprime(n)):
seq(a(n), n=1..15);  # Alois P. Heinz, May 30 2025

5^# - 3^# - 2^# &/@Prime[Range[20]] (* G. C. Greubel, Sep 30 2016 *)

a(n,p=prime(n))=5^p - 3^p - 2^p \\ Charles R Greathouse IV, Sep 30 2016

a(n) = 5^p - 3^p - 2^p, with p = A000040(n).

a(n) = A057902(n) - A057901(n) - A034785(n). - Michel Marcus, Jun 14 2014

More terms from Vincenzo Librandi, Dec 14 2010

A135174 a(n) = 5^prime(n) - 3^prime(n) + 2^prime(n).

Original entry on oeis.org

20, 106, 2914, 76066, 48653026, 1219116994, 762810444034, 19072324590946, 11920834820287906, 186264446293255209154, 4656612255406143777826, 72759575691550490581159234, 45474735052173417717604422274, 1136868376887903338795354772706, 710542735733511371652904252645666

Offset: 1

Omar E. Pol, Nov 25 2007

			a(4)=76066 because the 4th prime number is 7, 5^7=78125, 3^7=2187, 2^7=128 and 78125-2187+128=76066.

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A000040.

Cf. 2^p: A034785; 3^p: A057901; 5^p: A057902.

[5^p-3^p+2^p: p in PrimesUpTo(100)]; // Vincenzo Librandi, Dec 14 2010

Table[5^p-3^p+2^p,{p,Prime[Range[20]]}] (* Harvey P. Dale, Dec 12 2013 *)

a(n)= 5^A000040(n) - 3^A000040(n) + 2^A000040(n).

More terms from Vincenzo Librandi, Dec 14 2010

A135176 5^p + 3^p + 2^p, where p = prime(n).

Original entry on oeis.org

38, 160, 3400, 80440, 49007320, 1222305640, 763068724360, 19074649113880, 11921023106645560, 186264583554009938920, 4656613490752936345720, 72759576592118302363153960, 45474735125119410471945995080, 1136868377544417273584428927960, 710542735786689000370819259221240

Offset: 1

Omar E. Pol, Nov 25 2007

			a(4)=80440 because the 4th prime number is 7, 5^7=78125, 3^7=2187, 2^7=128 and 78125+2187+128=80440.

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. 2^p: A034785. 3^p: A057901. 2^5: A057902.

[5^p+3^p+2^p: p in PrimesUpTo(100)]; // Vincenzo Librandi Dec 14 2010

Table[5^p + 3^p + 2^p, {p, Prime[Range[20]]}] (* Vincenzo Librandi, May 24 2014 *)

p=A000040(n): a(n)= 5^p + 3^p + 2^p.

More terms from Vincenzo Librandi, Dec 14 2010

cp's OEIS Frontend

A057901 a(n) = 3^prime(n).

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A132797 Decimal expansion of Sum_{n >= 1} 1/5^prime(n).

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A135175 a(n) = 5^p + 3^p - 2^p, where p = prime(n).

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A269327 a(n) = 7^prime(n).

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A135173 a(n) = 5^p - 3^p - 2^p, where p = prime(n).

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Magma

Maple

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A135174 a(n) = 5^prime(n) - 3^prime(n) + 2^prime(n).

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Magma

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A135176 5^p + 3^p + 2^p, where p = prime(n).

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