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A242489 Smallest even k such that lpf(k-1) = prime(n), while lpf(k-3) > prime(n), where lpf=least prime factor (A020639). 9
10, 26, 50, 254, 170, 392, 362, 944, 842, 1892, 1370, 2420, 1850, 2210, 3764, 6314, 3722, 4892, 5042, 7082, 8612, 9380, 7922, 12320, 11414, 10610, 11450, 13844, 18872, 16130, 17162, 20414, 19322, 26672, 24614, 25592, 29504, 37910, 29930, 44930, 36020, 36482 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

This sequence is connected with a sufficient condition for the infinitude of twin primes.

Almost all numbers of the form a(n)-3 are primes. For composite numbers of such a form, see A242716.

Primes p for which a(p) = p^2+1 form sequence A062326 for p >= 3. - Vladimir Shevelev, May 21 2014

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 2..2501

FORMULA

a(n) >= prime(n)^2+1. - Vladimir Shevelev, May 21 2014

EXAMPLE

Let n=2, prime(2)=3. Then lpf(10-1)=3, but lpf(10-3)=7>3.

Since k=10 is the smallest such k, then a(2)=10.

MATHEMATICA

lpf[n_]:=lpf[n]=First[Select[Divisors[n], PrimeQ[#]&]];

Table[test=Prime[n]; NestWhile[#+2&, test^2+1, !((lpf[#-1]==test)&&(lpf[#-3]>test))&], {n, 2, 60}] (* Peter J. C. Moses, May 21 2014 *)

PROG

(PARI) a(n) = {k = 6; p = prime(n); while ((factor(k-1)[1, 1] != p) || (factor(k-3)[1, 1] <= p), k+= 2); k; } \\ Michel Marcus, May 16 2014

CROSSREFS

Cf. A001359, A006512.

Sequence in context: A134406 A099978 A242719 * A074789 A229308 A125075

Adjacent sequences:  A242486 A242487 A242488 * A242490 A242491 A242492

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 16 2014

EXTENSIONS

More terms from Michel Marcus, May 16 2014

STATUS

approved

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Last modified September 17 10:37 EDT 2019. Contains 327129 sequences. (Running on oeis4.)