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A253216 Smallest of four primes in arithmetic progression with common difference 6 and digit sum prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)