The On-Line Encyclopedia of Integer Sequences (OEIS)

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A283873

Smallest number that is the sum of n successive primes and also the sum of n successive semiprimes, n > 1.
(history; published version)

#16 by Alois P. Heinz at Fri Mar 24 11:10:12 EDT 2017

STATUS

editing

approved

#15 by Alois P. Heinz at Fri Mar 24 11:10:08 EDT 2017

MAPLE

issp:= n-> is(not isprime(n) and numtheory[bigomega](n)=2):

ithsp:= proc(n) option remember; local k; for k from 1+

`if`(n=1, 1, ithsp(n-1)) while not issp(k) do od; k

end:

ps:= proc(i, j) option remember;

ithprime(j)+`if`(i=j, 0, ps(i, j-1))

end:

ss:= proc(i, j) option remember;

ithsp(j)+`if`(i=j, 0, ss(i, j-1))

end:

a:= proc(n) option remember; local i, j, k, l, p, s;

i, j, k, l, p, s:= 1, n, 1, n, ps(1, n), ss(1, n);

do if p=s then return p

elif p<s then i:=i+1; j:=j+1; p:= ps(i, j)

else k:=k+1; l:=l+1; s:= ss(k, l)

fi od

end:

seq(a(n), n=2..50); # Alois P. Heinz, Mar 24 2017

#14 by Alois P. Heinz at Fri Mar 24 11:01:52 EDT 2017

LINKS

Alois P. Heinz, <a href="/A283873/b283873.txt">Table of n, a(n) for n = 2..1000</a>

#13 by Alois P. Heinz at Fri Mar 24 10:20:47 EDT 2017

DATA

24, 749, 48, 311, 690, 251, 2706, 2773, 6504, 1081, 2162, 1753, 11356, 6223, 1392, 2303, 9838, 637, 14510, 1995, 3154, 21459, 72960, 5691, 8140, 1475, 2350, 3647, 1593, 7607, 55074, 2719, 9852, 12143, 106562, 12615, 9036, 19883, 15438, 28369, 8560, 8415, 3831

EXTENSIONS

More terms from Alois P. Heinz, Mar 24 2017

STATUS

approved

editing

#12 by N. J. A. Sloane at Sun Mar 19 19:53:14 EDT 2017

STATUS

proposed

approved

#11 by Jon E. Schoenfield at Sat Mar 18 10:24:24 EDT 2017

STATUS

editing

proposed

Discussion

Sun Mar 19

03:37

Zak Seidov: Michel Marcus: some spaces
Me: thx

#10 by Jon E. Schoenfield at Sat Mar 18 10:24:13 EDT 2017

NAME

Smallest number that is the sum of n successive primes and also the sum of n successive semiprimes, n > 1.

EXAMPLE

a(2) = 24 = A000040(5) + A000040(6) = 11 + 13 = A001358(4) + A001358(5) = 10 + 14,

a(3) = 749 = A000040(53) + A000040(54) + A000040(55) = 241 + 251 + 257 = A001358(79) + A001358(80) + A001358(81) = 247 + 249 + 253.

STATUS

proposed

editing

#9 by Michel Marcus at Sat Mar 18 06:06:38 EDT 2017

STATUS

editing

proposed

#8 by Michel Marcus at Sat Mar 18 06:06:30 EDT 2017

CROSSREFS

Sum of k consecutive primes: A001043 k=2, A034961 k=3, A034963 k=4, A034964 k=5, A127333 k=6, A127334 k=7, A127335 k=8, A127336 k=9, A127337 k=10, A127338 k=11, A127339 k=12.

Discussion

Sat Mar 18

06:06

Michel Marcus: some spaces

#7 by Michel Marcus at Sat Mar 18 06:05:10 EDT 2017

EXAMPLE

a(2) = 24 = A000040(5)+A000040(6) = 11+13 = A001358(4)+A001358(5) = 10+14,

a(3) = 749 = A000040(53)+A000040(54)+A000040(55) = 241+251+257 = A001358(79)+A001358(80)+A001358(81) = 247+249+253.

STATUS

proposed

editing