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A073737

Sums of three successive terms form the odd primes.

1, 1, 1, 3, 3, 5, 5, 7, 7, 9, 13, 9, 15, 17, 11, 19, 23, 17, 21, 29, 21, 23, 35, 25, 29, 43, 29, 31, 47, 31, 35, 61, 35, 41, 63, 45, 43, 69, 51, 47, 75, 57, 49, 85, 59, 53, 87, 71, 65, 91, 73, 69, 97, 75, 79, 103, 81, 85, 105, 87, 89, 107, 97, 103, 111, 99, 107, 125, 105, 117

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) + a(n-1) + a(n-2) = n-th prime, where a(0)=1, a(-1)=0, a(-2)=0 and the 0th prime is taken to be 1.

EXAMPLE

At n=10, a(10) + a(9) + a(8) = 13 + 9 + 7 = 29 = p_10.

MATHEMATICA

a[0] = 1; a[-1] = 0; a[-2] = 0; p[0] = 1; p[n_?Positive] := Prime[n]; a[n_] := a[n] = p[n] - a[n-1] - a[n-2]; Table[a[n], {n, 0, 69}] (* Jean-François Alcover, Sep 30 2011 *)

nxt[{a_, b_, c_}]:={b, c, NextPrime[a+b+c]-(b+c)}; Transpose[NestList[nxt, {1, 1, 1}, 70]][[1]] (* Harvey P. Dale, Mar 15 2015 *)

PROG

(Haskell)

a073737 n = a073737_list !! (n-1)

a073737_list =

1 : 1 : zipWith (-) a065091_list

(zipWith (+) a073737_list $ tail a073737_list)

-- Reinhard Zumkeller, Aug 14 2011

CROSSREFS

Cf. A036467, A001223, A073736.

Cf. A065091, A000040.

Sequence in context: A175298 A245148 A339104 * A237716 A245147 A339103