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

1,1

Links

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

Michael S. Branicky, Python program

Example

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.

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 *)

Prog

(Python) # see link

Crossrefs

Intersection of A050936 and A097889.

Sequence in context: A217744 A115811 A110286 * A127526 A249764 A202522

Adjacent sequences: A254856 A254857 A254858 * A254860 A254861 A254862

Keyword

nonn,easy

Author

Altug Alkan, May 05 2016

Status

approved