

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




OFFSET

20,1


COMMENTS

For prime p, a 2ptwin 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 2ptwin peak.


REFERENCES

Various postings to mathfun mailing list, 19961997.


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 2ptwin peak, then so is (qx2p,qx), 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



