cp's OEIS Frontend

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.

A277607 Smallest of four consecutive primes in arithmetic progression with common difference 42 and all digit sums prime.

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%I A277607 #17 Oct 31 2016 13:34:45
%S A277607 5,47,157,227,317,337,557,2027,3037,3217,5147,6047,7457,12527,13757,
%T A277607 14657,20357,21017,23747,32057,35027,47417,57047,84137,115727,125627,
%U A277607 127247,136337,147137,149027,212057,219937,225257,230017,240047,242357,264137,284117,304127
%N A277607 Smallest of four consecutive primes in arithmetic progression with common difference 42 and all digit sums prime.
%e A277607 a(1) = 5: 5 + 42 = 47; 47 + 42 = 89; 89 + 42 = 131; all four are prime. Their digit sums 5, 4 + 7 = 11, 8 + 9 = 17 and 1 + 3 + 1 = 5 are also prime.
%e A277607 a(2) = 47: 47 + 42 = 89; 89 + 42 = 131; 131 + 42 = 173; all four are prime. Their digit sums  4 + 7 = 11, 8 + 9 = 17, 1 + 3 + 1 = 5 and 1 + 7 + 3 = 11 are also prime.
%t A277607 A277607 = {}; Do[d = 42; k = Prime[n]; k1 = k + d; k2 = k + 2 d; k3 = k + 3 d; If[PrimeQ[k1] && PrimeQ[k2] && PrimeQ[k3] && PrimeQ[Plus @@ IntegerDigits[k]] && PrimeQ[Plus @@ IntegerDigits[k1]] && PrimeQ[Plus @@ IntegerDigits[k2]] && PrimeQ[Plus @@ IntegerDigits[k3]], AppendTo[A25, k]], {n, 30000}]; A277607
%t A277607 FCPQ[n_] := Module[{a = n + 42, b = n + 84, c = n + 126}, AllTrue[{a, b, c}, PrimeQ] && AllTrue[Total /@ (IntegerDigits /@ {n, a, b, c}), PrimeQ]]; Select[Prime[Range[30000]], FCPQ]
%Y A277607 Cf. A000040, A033447, A062088, A253140.
%K A277607 nonn,base
%O A277607 1,1
%A A277607 _K. D. Bajpai_, Oct 31 2016