

A007443


Binomial transform of primes.
(Formerly M1436)


12



2, 5, 13, 33, 83, 205, 495, 1169, 2707, 6169, 13889, 30993, 68701, 151469, 332349, 725837, 1577751, 3413221, 7349029, 15751187, 33616925, 71475193, 151466705, 320072415, 674721797, 1419327223, 2979993519, 6245693407, 13068049163
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OFFSET

1,1


COMMENTS

Equals row sums of triangle A164738. Example: a(4) = 33 = sum of terms in row 4 of triangle A164738: (2, 3, 5, 3, 5, 7, 5, 3).  Gary W. Adamson, Aug 23 2009
It might have been more natural to define this sequence with offset 0, which would also make the formula simpler. Then a(n) would be the first term of the sequence obtained from the primes by applying n times the operation "take sums of successive terms", Ts(k) = s(k)+s(k+1).  M. F. Hasler, Jun 02 2017


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..3000 (terms 1..1000 from Vincenzo Librandi)
N. J. A. Sloane, Transforms


FORMULA

a(n) = Sum_{k=1..n} binomial(n1,k1)*prime(k).  M. F. Hasler, Jun 02 2017
G.f.: Sum_{k>=1} prime(k)*x^k/(1  x)^k.  Ilya Gutkovskiy, Apr 21 2019


MAPLE

a:=n>add(binomial(n1, k1)*ithprime(k), k=1..n): seq(a(n), n=1..30); # Muniru A Asiru, Oct 23 2018


PROG

(PARI) A007443(n)=sum(k=1, n, binomial(n1, k1)*prime(k)) \\ M. F. Hasler, Jun 02 2017


CROSSREFS

Cf. A164738.  Gary W. Adamson, Aug 23 2009
Cf. A001043, A096277, A096278, A096279. See A287915 for indices of primes.
First differences give A178167.
Sequence in context: A292507 A307465 A116703 * A120925 A086588 A077939
Adjacent sequences: A007440 A007441 A007442 * A007444 A007445 A007446


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, May 21 2010


STATUS

approved



