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 A062584 First occurrence of n in the decimal representation of primes. 19
 101, 11, 2, 3, 41, 5, 61, 7, 83, 19, 101, 11, 127, 13, 149, 151, 163, 17, 181, 19, 1201, 211, 223, 23, 241, 251, 263, 127, 281, 29, 307, 31, 1321, 233, 347, 353, 367, 37, 383, 139, 401, 41, 421, 43, 443, 457, 461, 47, 487, 149, 503, 151, 521, 53, 541, 557, 563 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(0) = 101 is the first term where a(n) has two more digits than n. a(665808) = 106658081 is the first term where a(n) has three more digits than n. For which n does a(n) first have four more digits than n? Is lim sup a(n)/n infinite? - Charles R Greathouse IV, Jun 23 2017 Decide how many elements you want to find. Then for every prime, check all substrings to see if they are the first to be in some n. If you've found all values a(n), then you want to stop. - David A. Corneth, Jun 24 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA a(n) = prime(A082058(n)). - Giovanni Resta, Apr 29 2017 EXAMPLE 0 first occurs in 101. 14 first occurs as a substring in 149. MATHEMATICA Do[k = 1; While[ StringPosition[ ToString[Prime[k]], ToString[n]] == {}, k++ ]; Print[ Prime[k]], {n, 0, 62} ] (* Second program *) Function[s, Table[FromDigits@ FirstCase[s, w_ /; SequenceCount[w, IntegerDigits@ n] > 0], {n, 0, 56}]]@ IntegerDigits@ Prime@ Range[10^4] (* Michael De Vlieger, Jun 24 2017 *) With[{prs=Prime[Range[300]]}, Table[SelectFirst[prs, SequenceCount[ IntegerDigits[#], IntegerDigits[ n]]>0&], {n, 0, 60}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 06 2018 *) PROG (Haskell) import Data.List (isInfixOf) a062584 n = head [p | p <- a000040_list, show n `isInfixOf` show p] -- Reinhard Zumkeller, Dec 29 2011 (PARI) build(root, prefixLen, suffixLen)=my(v=List(), t); for(i=10^(prefixLen-1)\1, 10^prefixLen-1, t=eval(Str(i, root))*10^suffixLen; for(n=t, t+10^suffixLen-1, listput(v, n))); Vec(v) buildLen(n, d)=my(v=[]); for(i=0, d, v=concat(v, build(n, i, d-i))); Set(v) a(n)=if(n==0, return(101)); my(d, v); while(1, v=buildLen(n, d); for(i=1, #v, if(isprime(v[i]), return(v[i]))); d++) \\ Charles R Greathouse IV, Jun 23 2017 (PARI) first(n) = my(res = vector(n), todo = n, g); forprime(p = 2, , d = digits(p); for(i=1, #d, if(d[i]!=0, g = d[i]; if(res[g]==0, res[g]=p; todo--); for(j=1, #d-i, g=10*g+d[i+j]; if(g>n, next(2)); if(res[g]==0, res[g]=p; todo--)))); if(todo==0, return(concat([101], res)))) \\ David A. Corneth, Jun 23 2017 CROSSREFS Cf. A082058, A018800, A060386. Similar to but different from A068164. E.g., a(133) = 4133, but A068164(133) = 1033. Sequence in context: A282199 A266460 A060386 * A085054 A084045 A085419 Adjacent sequences:  A062581 A062582 A062583 * A062585 A062586 A062587 KEYWORD easy,nonn,base,nice AUTHOR Jason Earls, Jul 03 2001 EXTENSIONS More terms from Lior Manor, Jul 08 2001 Corrected by Larry Reeves (larryr(AT)acm.org), Jul 10 2001 Further correction from Reinhard Zumkeller, Oct 14 2001 STATUS approved

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Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)