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Numbers that are both a sum and a product of two or more consecutive primes.
1

%I #39 Jun 07 2022 11:13:05

%S 15,30,77,143,210,221,323,1001,2310,4199,5767,7429,9797,10403,11021,

%T 12317,20711,22499,23707,25591,28891,30030,33263,34571,36863,38021,

%U 46189,47053,75067,77837,79523,82861,82919,89951,95477,99221,104927,111547,116939,136891,141367,145157,146969,154433

%N Numbers that are both a sum and a product of two or more consecutive primes.

%H Michael S. Branicky, <a href="/A254859/b254859.txt">Table of n, a(n) for n = 1..4381</a> (terms 1..644 from Amiram Eldar)

%H Michael S. Branicky, <a href="/A254859/a254859.py.txt">Python program</a>

%e 15 is a term because 15 = 3 + 5 + 7 = 3*5.

%e 30 is a term because 30 = 13 + 17 = 2*3*5.

%e 77 is a term because 77 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 7*11.

%t np = NextPrime; pro[n_] := Block[{e, f}, {f, e} = Transpose@ FactorInteger@ n; Length@ f > 1 && Union@ e == {1} && np@ Most@ f == Rest@ f]; seq[lim_] := Union[Reap[Block[{p = 2, q, s}, While[2 p < lim, q = np@p; s = p+q; While[s <= lim, If[pro@s, Sow@s]; q = np@q; s += q]; p = np@p]]][[2, 1]]]; seq[10^5] (* _Giovanni Resta_, May 05 2016 *)

%o (Python) # see link

%Y Intersection of A050936 and A097889.

%K nonn,easy

%O 1,1

%A _Altug Alkan_, May 05 2016