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A277607
Smallest of four consecutive primes in arithmetic progression with common difference 42 and all digit sums prime.
1
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
1,1
EXAMPLE
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.
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]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
K. D. Bajpai, Oct 31 2016
STATUS
approved