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 A260143 Runs of consecutive integers with same prime signature. 3
 2, 3, 14, 15, 21, 22, 33, 34, 35, 38, 39, 44, 45, 57, 58, 75, 76, 85, 86, 87, 93, 94, 95, 98, 99, 116, 117, 118, 119, 122, 123, 133, 134, 135, 136, 141, 142, 143, 145, 146, 147, 148, 158, 159, 171, 172, 177, 178, 201, 202, 203, 205, 206, 213, 214, 215, 217, 218, 219, 230, 231, 244, 245 (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 LINKS Charles R Greathouse IV, 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, arXiv:0803.2636 [math.NT], 2008. Eric Weisstein's World of Mathematics, Prime Signature OEIS Wiki, Prime signatures EXAMPLE Runs begin: (terms)         (prime signature) {2, 3},         [1] {14, 15},       [1,1] {21, 22},       [1,1] {33, 34, 35},   [1,1] {38, 39},       [1,1] {44, 45},       [1,2] {57, 58},       [1,1] {75, 76},       [1,2] {85, 86, 87},   [1,1] {93, 94, 95},   [1,1] {98, 99},       [1,2] ... MATHEMATICA Split[Range[2, 250], Sort[FactorInteger[#1][[All, 2]]] === Sort[FactorInteger[#2][[All, 2]]]&] // Select[#, Length[#] > 1&]& // Flatten PROG (PARI) is(n)=my(f=vecsort(factor(n)[, 2])); f==vecsort(factor(n-1)[, 2]) || f==vecsort(factor(n+1)[, 2]) \\ Charles R Greathouse IV, Jul 17 2015 (Python) from sympy import factorint def aupto(limit):     aset, prevsig = {2}, [1]     for k in range(3, limit+2):         sig = sorted(factorint(k).values())         if sig == prevsig: aset.update([k - 1, k])         prevsig = sig     return sorted(aset) print(aupto(250)) # Michael S. Branicky, Sep 20 2021 CROSSREFS Main sequence is A052213. Sequence in context: A244295 A032806 A225756 * A275303 A281500 A041009 Adjacent sequences:  A260140 A260141 A260142 * A260144 A260145 A260146 KEYWORD nonn,easy,tabf AUTHOR Jean-François Alcover, Jul 17 2015 STATUS approved

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Last modified January 20 03:25 EST 2022. Contains 350467 sequences. (Running on oeis4.)