A253232 Smallest of five consecutive primes in arithmetic progression with common difference 90 and equal digit sums.

61, 83, 89, 593, 1399, 2063, 2287, 2351, 2441, 3491, 5081, 5171, 5479, 6599, 9497, 12073, 16561, 17569, 21377, 23099, 23189, 28573, 29063, 32143, 36293, 36497, 36587, 39569, 49279, 61291, 62383, 65449, 66373, 71167, 72379, 75347, 81457, 88591, 92377, 94261, 104369

Offset

1,1

Comments

90 is the smallest common difference (d) to get a set of five consecutive primes in arithmetic progression {p, p+d, p+2d, p+3d, p+4d} having digit sums equal; for p < prime(10^5).

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

a(1) = 61: 61+90 = 151; 151+90 = 241; 241+90 = 331; 331+90 = 421; all five are prime. Their digit sums 6+1 = 1+5+1 = 2+4+1 = 3+3+1 = 4+2+1 = 7 are all equal.
a(2) = 83: 83+90 = 173; 173+90 = 263; 263+90 = 353; 353+90 = 443; all five are prime. Their digit sums 8+3 = 1+7+3 = 2+6+3 = 3+5+3 = 4+4+3 = 11 are all equal.

Mathematica

A253232 = {}; Do[d = 90; k = Prime[n]; k1 = k + d; k2 = k + 2 d; k3 = k + 3 d; k4 = k + 4 d; s = Plus @@ IntegerDigits[k]; s1 = Plus @@ IntegerDigits[k1]; s2 = Plus @@ IntegerDigits[k2]; s3 = Plus @@ IntegerDigits[k3]; s4 = Plus @@ IntegerDigits[k4]; If[PrimeQ[k1] && PrimeQ[k2] && PrimeQ[k3] && PrimeQ[k4] && s == s1 && s1 == s2 && s2 == s3 && s3 == s4, AppendTo[A253232, k]], {n, 50000}]; A253232
cd90Q[p_]:=Module[{q=p+90, r=p+180, s=p+270, t=p+360}, AllTrue[{p, q, r, s, t}, PrimeQ] && Length[Union[Total/@(IntegerDigits/@{p, q, r, s, t})]]==1]; Select[ Prime[ Range[ 10000]], cd90Q] (* Harvey P. Dale, May 13 2022 *)

Crossrefs

Cf. A000040, A033447, A062088, A253140.

Sequence in context: A139931 A325076 A353598 * A345239 A245759 A186457

Adjacent sequences: A253229 A253230 A253231 * A253233 A253234 A253235

Keyword

nonn,base

Author

K. D. Bajpai, Dec 29 2014

Status

approved