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 A074822 #33 Feb 16 2025 08:32:47 %S A074822 19,79,109,229,349,379,439,499,739,769,859,1009,1279,1429,1489,1549, %T A074822 1579,1609,1999,2239,2269,2389,2539,2659,2689,2749,3019,3079,3319, %U A074822 3529,3919,4129,4519,4639,4729,4789,4969,4999,5479,5569,5689,5779,5839,6199 %N A074822 Primes p such that p + 4 is prime and p == 9 (mod 10). %C A074822 From _Rémi Eismann_, May 14 2006; May 04 2007: (Start) %C A074822 Also primes for which k is equal to 5 in A117078. Examples: prime(9) = prime(8) + (prime(8) mod 5) = 19 + (19 mod 5)=23; prime(23) = prime(22) + (prime(22) mod 5) = 79 + (79 mod 5)=83; prime(1359) = prime(1358) + (prime(1358) mod 5) = 11239+ (11239 mod 5)=11243. %C A074822 The prime numbers in this sequence are of the form (10i-1) with i=(level(n)+1)/2, level(n) defined in A117563. %C A074822 Consider A117078: a(n) = smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists. Sequence gives values of prime(n) for which k=5. (End) %C A074822 p is the lesser member of cousin primes (p,p+4) such that p == 9 (mod 10). - _Muniru A Asiru_, Jul 03 2017 %H A074822 Remi Eismann, <a href="/A074822/b074822.txt">Table of n, a(n) for n = 1..10000</a> %H A074822 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CousinPrimes.html">Cousin Primes</a> %t A074822 Prime[ Select[ Range[1000], Prime[ # ] + 4 == Prime[ # + 1] && Mod[ Prime[ # ], 10] == 9 & ]] %t A074822 Transpose[Select[Partition[Prime[Range[820]],2,1],Last[#]-First[#] == 4 && Mod[ First[ #],10]==9&]][[1]] (* _Harvey P. Dale_, Oct 20 2011 *) %o A074822 (PARI) is(n)=n%30==19 && isprime(n+4) && isprime(n) \\ _Charles R Greathouse IV_, Jul 12 2017 %o A074822 (PARI) list(lim)=my(v=List(),p=19); forprime(q=23,lim+4, if(q-p==4 && p%30==19, listput(v,p)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Jul 12 2017 %Y A074822 Cf. A001223, A117078, A117563. %Y A074822 Intersection of A023200 and A030433. %K A074822 nonn,easy %O A074822 1,1 %A A074822 _Roger L. Bagula_, Sep 30 2002 %E A074822 Edited by _Robert G. Wilson v_ and _N. J. A. Sloane_, Oct 03 2002 %E A074822 Entry revised by _N. J. A. Sloane_, Feb 24 2007