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A009190 2p twin peaks: a(n) = least x with lpf(x) = lpf(x + 2p) = p = prime(n) and lpf(y) < p for all x < y < x + 2p, where lpf = least prime factor. 1
7310131732015251470110369, 2061519317176132799110061, 3756800873017263196139951, 6316254452384500173544921 (list; graph; refs; listen; history; text; internal format)
OFFSET

20,1

COMMENTS

For prime p, a 2p-twin peak is a number x such that lpf(x) = lpf(x+2p) = p and x < y < x+2p => lpf(y) < p. (lpf(n) = least prime factor of n). p = 71 is the smallest prime admitting a 2p-twin peak.

REFERENCES

Various postings to math-fun mailing list, 1996-1997.

LINKS

Table of n, a(n) for n=20..23.

Eric Weisstein's World of Mathematics, Twin peaks

FORMULA

a(n) < A002110(n)/2, since if (x,x+2p) is a 2p-twin peak, then so is (q-x-2p,q-x), where q=A034386(p). - M. F. Hasler, Jan 28 2014

PROG

(PARI) is_TwinPeak(x)={forstep(k=2, 2*p=factor(x)[1, 1], 2, factor(x+k, p)[1, 1]<p || return(k==2*p))} \\ M. F. Hasler, Jan 28 2014

CROSSREFS

lpf(n) = A020639(n).

Sequence in context: A104267 A113538 A280347 * A095444 A217416 A133849

Adjacent sequences:  A009187 A009188 A009189 * A009191 A009192 A009193

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 10 20:48 EST 2017. Contains 295856 sequences.