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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
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 (list; graph; refs; listen; history; text; internal format)
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 * A280180 A337995 A337994

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

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Last modified May 20 13:32 EDT 2022. Contains 353873 sequences. (Running on oeis4.)