This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A206045 #44 Apr 17 2025 12:42:10
%S A206045 1536160080,4911773580,25104552900,77375139660,83516678490,
%T A206045 100070721660,150365447400,300035001630,318652145070,369822103350,
%U A206045 377344636200,511688932650,580028072610,638663371710,701534299830,745828915650,776625236100,883476548850,925639075620,956863233690
%N A206045 Numbers d such that 11 + j*d is prime for j = 0 to 10.
%C A206045 Original name: Values of the difference d for 11 primes in arithmetic progression with the minimal start sequence {11 + j*d}, j = 0 to 10.
%C A206045 The computations were done without any assumptions on the form of d. 21st term is greater than 10^12.
%C A206045 All terms are multiples of 210=2*3*5*7. - _Zak Seidov_, May 16 2015
%C A206045 Equivalently, integers d such that the longest possible arithmetic progression (AP) of primes with common difference d has exactly 11 elements (see example). These 11 elements are not necessarily consecutive primes. In fact, here, for each term d, there exists only one such AP of primes, and this one always starts with A342309(d) = 11, so this unique AP is (11, 11+d, 11+2d, 11+3d, 11+4d, 11+5d, 11+6d, 11+7d, 11+8d, 11+9d, 11+10d). - _Bernard Schott_, Mar 08 2023
%D A206045 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 139.
%H A206045 Zak Seidov, <a href="/A206045/b206045.txt">Table of n, a(n) for n = 1..623</a>.
%H A206045 Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a1-pot-pourri/3940-a1880-np-en-pa">A1880. NP en PA</a> (prime numbers in arithmetic progression) (in French).
%H A206045 Sameen Ahmed Khan, <a href="http://arxiv.org/abs/1203.2083">Primes in Geometric-Arithmetic Progression</a>, arXiv preprint arXiv:1203.2083 [math.NT], 2012.
%H A206045 Wikipedia, <a href="https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.
%H A206045 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>.
%F A206045 m is a term iff A123556(m) = 11. - _Bernard Schott_, Mar 08 2023
%e A206045 d = 4911773580 then {11, 4911773591, 9823547171, 14735320751, 19647094331, 24558867911, 29470641491, 34382415071, 39294188651, 44205962231, 49117735811} which is 11 primes in arithmetic progression.
%t A206045 a = 11; Do[If[PrimeQ[{a, a + d, a + 2*d, a + 3*d, a + 4*d, a + 5*d, a + 6*d, a + 7*d, a + 8*d, a + 9*d, a + 10*d}] == {True, True, True, True, True, True, True, True, True, True, True}, Print[d]], {d, 210,10^12, 210}] (* corrected by _Zak Seidov_, May 16 2015 *)
%t A206045 Select[Range[210,10^12,210],AllTrue[Range[0,10]#+11,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 28 2016 *)
%o A206045 (PARI) is(n)=for(j=1,10, if(!isprime(j*n+11), return(0))); 1 \\ _Charles R Greathouse IV_, May 18 2015
%Y A206045 Cf. A040976, A206038, A206040, A206042, A206043, A206044.
%Y A206045 Cf. A123556, A173919.
%Y A206045 Common differences for longest possible APs of primes with exactly k elements: A007921 (k=1), A359408 (k=2), A206037 (k=3), A359409 (k=4), A206039 (k=5), A359410 (k=6), A206041 (k=7), A360146 (k=10), this sequence (k=11).
%K A206045 nonn
%O A206045 1,1
%A A206045 _Sameen Ahmed Khan_, Feb 03 2012
%E A206045 New name from _Charles R Greathouse IV_, May 18 2015