A253216 Smallest of four primes in arithmetic progression with common difference 6 and digit sum prime.

1091, 15791, 30091, 369991, 421691, 501191, 661091, 1101091, 1539991, 2042591, 2210291, 2542091, 2811191, 3351191, 3512291, 3864691, 4411391, 4675591, 5960791, 5992291, 5998691, 6884191, 6918391, 7516891, 8608591, 8697791, 9297091, 9622891, 9646291, 12013091

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..2500

Example

a (1) = 1091: 1091 + 6 = 1097; 1097 + 6 = 1103; 1103 + 6 = 1109; all four are prime. Their digit sums 1+0+9+1 = 11; 1+0+9+7 = 17; 1+1+0+3 = 5 and 1+1+0+9 = 11 are also prime.
a(2) = 15791: 15791 + 6 = 15797; 15797 + 6 = 15803; 15803 + 6 = 15809; all four are prime. Their digit sums 1+5+7+9+1 = 23, 1+5+7+9+7 = 29, 1+5+8+0+3 = 17 and 1+5+8+0+9 = 23 are also prime.

Mathematica

A253216 = {}; Do[d = 6; k = Prime[n]; k1 = k + d; k2 = k + 2d; k3 = k + 3d; If[PrimeQ[k1] && PrimeQ[k2] && PrimeQ[k3] && PrimeQ[Plus @@ IntegerDigits[k]] && PrimeQ[Plus @@ IntegerDigits[k1]] && PrimeQ[Plus @@ IntegerDigits[k2]] && PrimeQ[Plus @@ IntegerDigits[k3]], AppendTo[A253216, k]], {n, 1000000}]; A253216
prQ[{a_, b_, c_, d_}]:=AllTrue[{b, c, d}, PrimeQ]&&AllTrue[Total/@ (IntegerDigits/@ {a, b, c, d}), PrimeQ]; Select[#+{0, 6, 12, 18}& /@Prime[Range[800000]], prQ][[All, 1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 26 2018 *)

Prog

(PARI) for( n=1, 10^6, k=prime(n); k1=k+6; k2=k+12; k3=k+18; if(isprime(k1)&isprime(k2)&isprime(k3) &isprime(eval(Str(sumdigits(k)))) &isprime(eval(Str(sumdigits(k1)))) &isprime(eval(Str(sumdigits(k2)))) &isprime(eval(Str(sumdigits(k3)))), print1(k, ", ")))

Crossrefs

Cf. A000040, A033447, A062088, A253140.

Sequence in context: A031531 A161118 A031711 * A210301 A043597 A043837

Adjacent sequences: A253213 A253214 A253215 * A253217 A253218 A253219

Keyword

nonn,base

Author

K. D. Bajpai, Dec 29 2014

Extensions

Definition corrected by Harvey P. Dale, May 26 2018

Status

approved