A105418 Smallest prime p such that the sum of it and the following prime have n prime factors including multiplicity, or 0 if no such prime exists.

2, 0, 3, 11, 53, 71, 61, 191, 953, 1151, 3833, 7159, 4093, 30713, 36857, 110587, 360439, 663547, 2064379, 786431, 3932153, 5242877, 9437179, 63700991, 138412031, 169869311, 436207613, 3875536883, 1358954453, 1879048183, 10066329587, 8053063661, 14495514619

Offset

1,1

Comments

a(2) = 0 since it is impossible.

Links

Amiram Eldar, Table of n, a(n) for n = 1..38

Example

a(5) = 53 because (53 + 59) = 112 = 2^4*7.
a(24) = 63700991 because (63700991 + 63700993) = 127401984 = 2^19*3^5.
a(28) = 3875536883 because (3875536883 + 3875536909) = 7751073792 = 2^25*3*7*11.
a(29) = 1358954453 because (1358954453 + 1358954539) = 2717908992 = 2^25*3^4.
a(30) = 1879048183 because (1879048183 + 1879048201) = 3758096384 = 2^29*7.

Mathematica

f[n_] := Plus @@ Flatten[ Table[ #[[2]], {1}] & /@ FactorInteger[n]]; t = Table[0, {40}]; Do[a = f[Prime[n] + Prime[n + 1]]; If[a < 41 && t[[a]] == 0, t[[a]] = Prime[n]; Print[{a, Prime[n]}]], {n, 111500000}]; t

Crossrefs

Cf. A001043, A001222, A071215, A098037, A098048.

Sequence in context: A325816 A121065 A077928 * A368584 A368583 A365547

Adjacent sequences: A105415 A105416 A105417 * A105419 A105420 A105421

Keyword

nonn

Author

Giovanni Teofilatto and Robert G. Wilson v, Apr 06 2005

Extensions

a(28)=3875536883 from Ray Chandler and Robert G. Wilson v, Apr 10 2005

Edited by Ray Chandler, Apr 10 2005

a(31)-a(33) from Daniel Suteu, Nov 18 2018

Status

approved