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A054859 Smallest integer that can be expressed as the sum of consecutive primes in exactly n ways. 9
1, 2, 5, 41, 1151, 311, 34421, 218918, 3634531, 48205429 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

R. K. Guy, Unsolved Problems In Number Theory, C2.

LINKS

Table of n, a(n) for n=0..9.

Leo Moser, Notes on number theory. III. On the sum of consecutive primes, Canad. Math. Bull. 6 (1963), pp. 159-161.

C. Rivera, Some terms and related problem

EXAMPLE

41 = 41 = 11+13+17 = 2+3+5+7+11+13, 41 is the smallest number expressible in 3 ways, so a(3)=41.

From Robert G. Wilson v, Feb 21 2011: (Start)

a(0) = 1 because 1 cannot be expressed as the sum of any set of consecutive primes,

a(1) = 2 because 2 is the first prime,

a(2) = 5 because 2+3 = 5,

a(4) = 1151 because 7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79+83+89+97+101 = 223+227+229+233+239 = 379+383+389 = 1151,

a(5) = 311 because 11+13+17+19+23+29+31+37+41+43+47 = 31+37+41+43+47+53+59 = 53+59+61+67+71 = 101+103+107 = 311,

a(6) = 34421 because  269+271+...+701+709 = 1429+1433+...+1567+1571 = 3793+3797+3803+3821+3823+3833+3847+3851+3853 = 4889+4903+4909+4919+4931+4933+4937 = 11467+11471+11483 = 34421,

a(7) = 218918 because 3301+3307+...+3767+3769 = 4561+4567+...+4951+4957 = 5623+5639+...+5881+5897 = 7691+7699+...+7933+7937 = 9851+9857+...+10067+10069  = 13619+13627+...+13723+13729 = 18199+18211+...+18287+18289,

a(8) = 3634531 because 313+317+...+7873+7877 = 977+983+...+7933+7937 = 31567+31573+...+32707+32713 = 70997+70999+...+71479+71483 = 73897+73907+...+74413+74419 = 172969+172973+...+173189+173191 = 519161+519193+...+519247+519257 = 3634531,

a(9) = 48205429 because 124291+124297+...+128747+128749 = 176303+176317+...+179453+179461 = 331537+331543+...+333383+333397 = 433577+433607+...+434933+434939 = 541061+541087+...+542141+542149 = 2536943+2536991+...+2537303+2537323 = 16068461+16068469+16068499 = 48205429, etc. (End)

MATHEMATICA

lmt = 500000000; p = Prime@ Range@ PrimePi@ lmt; t = Table[0, {lmt}]; Do[s = 0; j = i; While[s = s + p[[j]]; s <= lmt, t[[s]]++; j++], {i, Length@ p}]; Table[ Position[t, n, 1, 1], {n, 0, 0}] (* Robert G. Wilson v, Feb 21 2011 *)

CROSSREFS

Cf. A054845.

Sequence in context: A175172 A218057 A126469 * A076725 A059917 A255963

Adjacent sequences:  A054856 A054857 A054858 * A054860 A054861 A054862

KEYWORD

nonn

AUTHOR

Jud McCranie, May 25 2000

EXTENSIONS

a(10) > 1500000000 if it exists.

STATUS

approved

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Last modified June 26 02:24 EDT 2017. Contains 288749 sequences.