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A052213 Numbers n with prime signature(n) = prime signature(n+1). 8
2, 14, 21, 33, 34, 38, 44, 57, 75, 85, 86, 93, 94, 98, 116, 118, 122, 133, 135, 141, 142, 145, 147, 158, 171, 177, 201, 202, 205, 213, 214, 217, 218, 230, 244, 253, 285, 296, 298, 301, 302, 326, 332, 334, 375, 381, 387, 393, 394, 429, 434, 445, 446, 453, 481 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is infinite, see A189982 and Theorem 4 in Goldston-Graham-Pintz-Yıldırım. - Charles R Greathouse IV, Jul 17 2015

This is a subsequence of A005237, hence a(n) >> n sqrt(log log n) by the Erdős-Pomerance-Sárközy result cited there. - Charles R Greathouse IV, Jul 17 2015

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

D. A. Goldston, S. W. Graham, J. Pintz, and C. Y. Yıldırım, Small gaps between almost primes, the parity problem, and some conjectures of Erdos on consecutive integers (2008)

MathOverflow, Question on consecutive integers with similar prime factorizations

EXAMPLE

14 = 2^1*7^1 and 15 = 3^1*5^1, so both have prime signature {1,1}.

MATHEMATICA

pri[n_] := Sort[ Transpose[ FactorInteger[n]] [[2]]]; Select[ Range[ 2, 1000], pri[#] == pri[#+1] &]

PROG

(PARI) lista(nn) = for (n=1, nn-1, if (vecsort(factor(n)[, 2]) == vecsort(factor(n+1)[, 2]), print1(n, ", ")); ); \\ Michel Marcus, Jun 10 2015

CROSSREFS

Cf. A005237, A189982.

Sequence in context: A138047 A005237 A140578 * A086263 A073143 A066613

Adjacent sequences:  A052210 A052211 A052212 * A052214 A052215 A052216

KEYWORD

easy,nonn,changed

AUTHOR

Erich Friedman, Jan 29 2000

STATUS

approved

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Last modified July 27 21:36 EDT 2015. Contains 260030 sequences.