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A157733 a(0)=2, a(1)=3. Then 2 or 22 followed by a string of 3's such that the sum of the digits of a(n) is equal to prime(n). 1
2, 3, 23, 223, 2333, 22333, 233333, 2233333, 23333333, 2333333333, 22333333333, 2233333333333, 23333333333333, 223333333333333, 2333333333333333, 233333333333333333, 23333333333333333333, 223333333333333333333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

We search for w twos and t threes in prime(n) = 2*w + 3*t. If t = floor(prime(n)/3) would lead to w = 1/2, we decrease t by 1.

The number of twos is 3 - A039701(n) if n > 1.

If prime(n) is congruent to 1 mod 6, then a(n) starts with 22, but if prime(n) is congruent to 5 mod 6, then a(n) starts with 2. - Alonso del Arte, Dec 04 2013

LINKS

Table of n, a(n) for n=0..17.

EXAMPLE

a(3) = 23 because the third prime is 5 and 2 + 3 = 5.

a(4) = 223 because the fourth prime is 7 and 2 + 2 + 3 = 7.

a(5) = 2333 because the fifth prime is 11 and 2 + 3 + 3 + 3 = 11.

MATHEMATICA

Module[{nn = 30, t1, t2}, t1 = FromDigits/@Select[Table[PadRight[{2}, n, 3], {n, 2, nn}], PrimeQ[Total[#]] &]; t2 = FromDigits/@Select[Table[PadRight[{2, 2}, n, 3], {n, 2, nn}], PrimeQ[Total[#]] &]; Union[Join[{2, 3}, t1, t2]]] (* Harvey P. Dale, Mar 06 2013 *)

CROSSREFS

Cf. A139067, A157966.

Sequence in context: A020458 A139067 A099656 * A235934 A064888 A104458

Adjacent sequences:  A157730 A157731 A157732 * A157734 A157735 A157736

KEYWORD

nonn,base

AUTHOR

Paul Curtz, Mar 05 2009

EXTENSIONS

Edited by R. J. Mathar, Mar 15 2009

STATUS

approved

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Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)