A254859 Numbers that are both a sum and a product of two or more consecutive primes.

15, 30, 77, 143, 210, 221, 323, 1001, 2310, 4199, 5767, 7429, 9797, 10403, 11021, 12317, 20711, 22499, 23707, 25591, 28891, 30030, 33263, 34571, 36863, 38021, 46189, 47053, 75067, 77837, 79523, 82861, 82919, 89951, 95477, 99221, 104927, 111547, 116939, 136891, 141367, 145157, 146969, 154433

Offset: 1

Author

Altug Alkan, May 05 2016

Keywords

• nonn
• easy

Examples

			15 is a term because 15 = 3 + 5 + 7 = 3*5.
30 is a term because 30 = 13 + 17 = 2*3*5.
77 is a term because 77 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 7*11.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..4381 (terms 1..644 from Amiram Eldar)
• Michael S. Branicky, Python program

Crossrefs

Intersection of A050936 and A097889.

Programs

Mathematica

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 *)

Python

# see link