The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A218114 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A218114

Integer arithmetic means of 10 consecutive primes.
(history; published version)

#30 by R. J. Mathar at Mon Apr 24 12:30:32 EDT 2023

STATUS

editing

approved

#29 by R. J. Mathar at Mon Apr 24 12:30:29 EDT 2023

NAME

Integer arithmetical averages arithmetic means of 10 consecutive primes.

COMMENTS

Primes are listed in A123096 = (727, 761, 1663, 1783, 1811, ...).

EXAMPLE

a(1) is derived from (prime(6)+...+prime(15))/10 = (13+ 17+ 19+ 23+ 29+ 31+ 37+ 41+ 43+ 47)/10=30.

CROSSREFS

Cf. A000040, A123096, (subsequence of primes), A127337.

STATUS

approved

editing

#28 by Harvey P. Dale at Sat Aug 28 18:27:46 EDT 2021

STATUS

editing

approved

#27 by Harvey P. Dale at Sat Aug 28 18:27:41 EDT 2021

MATHEMATICA

Select[Mean/@Partition[Prime[Range[300]], 10, 1], IntegerQ] (* Harvey P. Dale, Aug 28 2021 *)

STATUS

approved

editing

#26 by Alois P. Heinz at Sun May 24 08:26:57 EDT 2015

STATUS

editing

approved

#25 by Alois P. Heinz at Sun May 24 08:26:53 EDT 2015

COMMENTS

Also difference 5 seem seems to occur infinitely often. For first 200000 differences, values 5..10 occur 5, 57, 123, 400, 1755, 1439 times . Apparently all differences >4 occur infinitely often. - Zak Seidov, May 22 2015

STATUS

proposed

editing

#24 by Michel Marcus at Sat May 23 04:48:50 EDT 2015

STATUS

editing

proposed

#23 by Michel Marcus at Sat May 23 04:48:38 EDT 2015

PROG

(PARI) lista(nn) = {for (n=1, nn, my(s = sum(k=0, 9, prime(n+k))/10); if (type(s) == "t_INT", print1(s, ", ")); ); } \\ Michel Marcus, May 23 2015

STATUS

proposed

editing

#22 by Michel Marcus at Sat May 23 04:48:03 EDT 2015

STATUS

editing

proposed

#21 by Michel Marcus at Sat May 23 04:47:56 EDT 2015

PROG

(PARI) lista(nn) = {for (n=1, nn, s = sum(k=0, 9, prime(n+k))/10; if (type(s) == "t_INT", print1(s, ", ")); ); } \\ Michel Marcus, May 23 2015

STATUS

proposed

editing