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 A023186 Lonely (or isolated) primes: increasing distance to nearest prime. 25
 2, 5, 23, 53, 211, 1847, 2179, 3967, 16033, 24281, 38501, 58831, 203713, 206699, 413353, 1272749, 2198981, 5102953, 10938023, 12623189, 72546283, 142414669, 162821917, 163710121, 325737821, 1131241763, 1791752797, 3173306951, 4841337887, 6021542119, 6807940367, 7174208683, 8835528511, 11179888193, 15318488291, 26329105043, 31587561361, 45241670743 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Erdős and Suranyi call these reclusive primes and prove that there are an infinite number of them. They define these primes to be between two primes. Hence their first term would be 3 instead of 2. Record values in A120937. - T. D. Noe, Jul 21 2006 REFERENCES Paul Erdős and Janos Suranyi, Topics in the theory of numbers, Springer, 2003. LINKS Dmitry Petukhov, Table of n, a(n) for n = 1..56 (first 40 terms from Ken Takusagawa, terms 41..52 from Giovanni Resta) EXAMPLE The nearest prime to 23 is 4 units away, larger than any previous prime, so 23 is in the sequence. The prime a(4) = A120937(3) = 53 is at distance 2*3 = 6 from its neighbors {47, 59}. The prime a(5) = A120937(4) = A120937(5) = A120937(6) = 211 is at distance 2*6 = 12 from its neighbors {199, 223}. Sequence A120937 requires the terms to have 2 neighbors, therefore its first term is 3 and not 2. - M. F. Hasler, Dec 28 2015 MAPLE P:=proc(q) local a, b, k, n; print(2); k:=0; for n from 3 to q do a:=ithprime(n)-prevprime(ithprime(n)); b:=nextprime(ithprime(n))-ithprime(n); if a>b then if k i, Print[q]; i = m]; p = q; q = r, {n, 1, 152382000}] Join[{2}, DeleteDuplicates[{#[], Min[Differences[#]]}&/@Partition[Prime[ Range[ 2, 10^6]], 3, 1], GreaterEqual[ #1[], #2[]]&][[;; , 1]]] (* The program generates the first 20 terms of the sequence. *) (* Harvey P. Dale, Aug 31 2023 *) CROSSREFS Related sequences: A023186, A023187, A023188, A046929, A046930, A046931, A051650, A051652, A051697-A051702, A051728, A051729, A051730, A102723. The distances are in A023187. Sequence in context: A156314 A308055 A173396 * A023188 A106858 A290887 Adjacent sequences: A023183 A023184 A023185 * A023187 A023188 A023189 KEYWORD nonn,nice AUTHOR David W. Wilson EXTENSIONS More terms from Jud McCranie, Jun 16 2000 More terms from T. D. Noe, Jul 21 2006 STATUS approved

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Last modified September 28 02:54 EDT 2023. Contains 365714 sequences. (Running on oeis4.)