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 A138198 First occurrence of prime gaps which are squares. 5
 2, 7, 1831, 9551, 89689, 396733, 11981443, 70396393, 1872851947, 10958687879, 47203303159, 767644374817, 8817792098461, 78610833115261, 497687231721157, 2069461000669981, 22790428875364879, 78944802602538877 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS More precisely, consider the possible squares which can occur as prime gaps: g_0=1, g_1=2^2, g_2=4^2, g_3=6^2, g_4=8^2, ... Then a(n) = smallest prime p(i) such that p(i+1)-p(i) = g_n, or a(n) = -1 if the gap g_n never occurs. - N. J. A. Sloane, Oct 28 2016 LINKS EXAMPLE Notes by Thomas R. Nicely: No gap exceeding 1442 has been definitively established as a first occurrence; larger gaps included in these lists are instead first occurrences presently known of prime gaps. The smallest gap whose first occurrence remains uncertain is the (nonsquare) gap of 1208. prime,gap 2, 1=1^2 7, 4=2^2 1831, 16=4^2 9551, 36=6^2 89689, 64=8^2 396733, 100=10^2 11981443, 144=12^2 70396393, 196=14^2 1872851947, 256=16^2 10958687879, 324=18^2 47203303159, 400=20^2 767644374817, 484=22^2 8817792098461, 576=24^2 78610833115261, 676=26^2 497687231721157, 784=28^2 2069461000669981, 900=30^2 22790428875364879, 1024=32^2 78944802602538877, 1156=34^2 2980374211158121907, 1296=36^2 18479982848279580912452968237, 1444=38^2 10338270318362067887873513954823823, 1600=40^2 5462539353768233509094313080601639583, 1764=42^2 9634432076725832064810529394509018411, 1936=44^2 24103660699017475735076387748469761375352177, 2116=46^2 1171872038536282864481405693168029955108099, (*48^2*) 169512938487733553802932479078305855585466971701227, (*50^2*) 228422210024736896126707605155690522381875250546666532046327, (*52^2*) 7229972437439469171089374324333535009566526827968927563, (*54^2*) 1263895714932859021916447978075625934206362807439043695674222113, (*56^2*) 569493611436727594340298806603382857255173440636060754222617328828425379, (*58^2*) 281376087412013738611508677824321032930454474305215907812114263492815921, (*60^2*) 680561565394793619717614472954048053005171290126070180152868857556290989645629867 (*62^2*) MATHEMATICA Function[w, Prime@ First@ # & /@ Map[w[[ Key@ # ]] &, Select[Keys@ w, IntegerQ@ Sqrt@ # &]]]@ PositionIndex@ Differences@ Prime@ Range[10^7] (* Michael De Vlieger, Oct 27 2016 *) PROG (PARI) a(n)=my(k=max(1, 4*(n-1)^2), p=2); forprime(q=3, , if(q-p==k, return(p)); p=q) \\ Charles R Greathouse IV, Jun 05 2013 CROSSREFS Sequence in context: A000653 A128847 A123180 * A320505 A144836 A174308 Adjacent sequences:  A138195 A138196 A138197 * A138199 A138200 A138201 KEYWORD nonn AUTHOR Zak Seidov, Mar 05 2008 EXTENSIONS Edited by N. J. A. Sloane, Oct 28 2016 Misprints in EXAMPLE fixed by Zak Seidov, Oct 18 2018 STATUS approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)