A062337 Primes whose sum of digits is 7.

7, 43, 61, 151, 223, 241, 313, 331, 421, 601, 1033, 1051, 1123, 1213, 1231, 1303, 1321, 2113, 2131, 2203, 2221, 2311, 3121, 3301, 4003, 4021, 4111, 4201, 5011, 5101, 10141, 10303, 10321, 10501, 11113, 11131, 11311, 12211, 12301, 13003, 14011

Offset

1,1

Comments

There are O((log n)^6) members of this sequence below n.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

Intersection of A000040 (primes) and A052221 (digit sum 7). - M. F. Hasler, Mar 09 2022

Example

601 is a prime with sum of the digits = 7, hence belongs to the sequence.

Mathematica

Select[Prime[Range[3000]], Plus @@ IntegerDigits[ # ] == 7 &] (Zak Seidov, Feb 17 2005)

Prog

(PARI) A062337(lim)={my(pow=ceil(log(floor(lim)-.5)/log(10)), n); print("Checking for members of A062337 up to 10^"pow); for(a=0, pow-1, for(b=0, a, for(c=0, b, for(d=0, c, for(e=0, d, for(f=0, e, n=10^a+10^b+10^c+10^d+10^e+10^f+1; if(isprime(n), print1(n", "))))))))};
(PARI) SumD(x)= { s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } { default(primelimit, 2*10^8); n=0; forprime (p=2, 2*10^8, if (SumD(p) == 7, write("b062337.txt", n++, " ", p); if (n==500, break)) ) } \\ Harry J. Smith, Aug 05 2009
From M. F. Hasler, Mar 09 2022: (Start)
(PARI) select( {is_A062337(p, s=7)=sumdigits(p)==s&&isprime(p)}, primes([1, 14321])) \\ 2nd optional parameter for similar sequences with other digit sums.
(PARI) {A062337_upto_length(L, s=7, a=List(), u=[10^(L-k)|k<-[1..L]])=forvec(d=[[1, L]|i<-[1..s]], isprime(p=vecsum(vecextract(u, d))) && listput(a, p), 1); Vecrev(a)} \\ (End)
(Magma) [p: p in PrimesUpTo(250000) | &+Intseq(p) eq 7]; // Vincenzo Librandi, Jul 08 2014

Crossrefs

Subsequence of A062336. See also A000579.

Cf. similar sequences listed in A244918.

Sequence in context: A243459 A301628 A061241 * A176252 A118703 A139832

Adjacent sequences: A062334 A062335 A062336 * A062338 A062339 A062340

Keyword

nonn,base,easy

Author

Amarnath Murthy, Jun 21 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jul 06 2001

Comments and program from Charles R Greathouse IV, Sep 11 2009

Status

approved