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

5, 47, 157, 227, 317, 337, 557, 2027, 3037, 3217, 5147, 6047, 7457, 12527, 13757, 14657, 20357, 21017, 23747, 32057, 35027, 47417, 57047, 84137, 115727, 125627, 127247, 136337, 147137, 149027, 212057, 219937, 225257, 230017, 240047, 242357, 264137, 284117, 304127

Offset: 1

Author

K. D. Bajpai, Oct 31 2016

Keywords

• nonn
• base

Examples

			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.
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.
		

Crossrefs

Cf. A000040, A033447, A062088, A253140.

Programs

Mathematica

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
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]