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A227856 Sequence of pairs k,g with k<3*2^n the smallest such that 3*2^n+k, 3*2^n+k+g, 3*2^n+k+2*g are three consecutive primes in arithmetic progression starting at n=5 as there is not any solution for n<5 1
55, 6, 7, 12, 173, 6, 173, 6, 205, 6, 229, 6, 113, 6, 203, 6, 95, 6, 475, 6, 163, 6, 119, 12, 377, 18, 1045, 6, 133, 12, 551, 24, 131, 12, 259, 6, 1105, 42, 539, 6, 1487, 18, 1295, 12, 5, 12, 289, 36, 311, 36, 269, 6, 2833, 6, 1813, 18, 835, 6, 319, 6, 587, 6, 239, 30, 1225, 6, 1825, 12, 973, 12, 89, 30, 551, 12, 1805, 30, 1039, 18, 1219, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

COMMENTS

The ratio k/n^2 is in average near 0.8 and < 7 for n<701.

The ratio g/n^2 is in average near 0.5 and < 4 for n<701.

If 3*2^n+k > 10^22 the numbers are probable primes.

LINKS

Pierre CAMI, Table of n, a(n) for n = 5..1396

EXAMPLE

3*2^5+55=151, 3*2^5+55+6=157 3*2^5+55*2*6=163

151, 157, 163 three consecutive primes in arithmetic progression 6, so first pair is 55, 6

PROG

PFGW & SCRIPTIFY

SCRIPT

DIM i

DIM j

DIM k

DIM n, 4

DIM pp

DIM qq

DIM rr

DIMS t

OPENFILEOUT myf, a(n).txt

LABEL loop1

SET n, n+1

SET i, -1

SET j, 0

SET k, 0

LABEL a

SET i, i+2

SETS t, %d, %d\,; n; i

SET pp, 3*2^n+i

PRP pp, t

IF ISPRP THEN GOTO b

GOTO a

LABEL b

SET j, j+2

SETS t, %d, %d, %d\,; n; i; j

SET qq, pp+j

PRP qq, t

IF ISPRP THEN GOTO c

GOTO b

LABEL c

SET k, k+2

SETS t, %d, %d, %d, %d\,; n; i; j; k

SET rr, qq+k

PRP rr, t

IF ISPRP THEN GOTO d

GOTO c

LABEL d

IF j==k THEN GOTO x

SET i, i+j

SET pp, qq

SET j, 0

SET k, 0

GOTO b

LABEL x

WRITE myf, t

GOTO loop1

CROSSREFS

Cf. A230699, A230852

Sequence in context: A159732 A174946 A182119 * A057965 A083516 A203907

Adjacent sequences:  A227853 A227854 A227855 * A227857 A227858 A227859

KEYWORD

nonn

AUTHOR

Pierre CAMI, Nov 01 2013

STATUS

approved

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Last modified December 5 10:11 EST 2021. Contains 349543 sequences. (Running on oeis4.)